% General books

@book {HopcroftUllman,
	AUTHOR = {Hopcroft, John E. and Ullman, Jeffrey D.},
	TITLE = {Introduction to automata theory, languages, and computation},
	NOTE = {Addison-Wesley Series in Computer Science},
	PUBLISHER = {{Addison-Wesley Publishing Co., Reading, Mass.}},
	YEAR = {1979},
	PAGES = {x+418},
}

@book {Knuth-TAOCP3,
	AUTHOR = {Donald~E.~Knuth},
	TITLE = {The art of computer programming. {V}olume 3},
	NOTE = {Sorting and searching, Addison-Wesley Series in Computer Science and Information Processing},
	PUBLISHER = {{Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont.}},
	YEAR = {1973},
	PAGES = {xi+722 pp. (1 foldout)},
}

@book {Knuth-TAOCP1,
	AUTHOR = {Knuth, Donald E.},
	TITLE = {The art of computer programming. {V}ol. 1: {F}undamental algorithms},
	SERIES = {Second printing},
	PUBLISHER = {{Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont}},
	YEAR = {1969},
	PAGES = {xxi+634},
}

@book{DeLoeraRambauSantos,
	AUTHOR = {Jesus~A.~{De Loera} and J\"org~Rambau and Francisco~Santos},
	TITLE = {Triangulations: Structures for Algorithms and Applications},
	PUBLISHER = {Springer Verlag},
	YEAR = {2010},
	VOLUME = {25},
	SERIES = {Algorithms and {C}omputation in Mathematics},
}

@book {Ziegler-polytopes,
	AUTHOR = {G{\"u}nter~M.~Ziegler},
	TITLE = {Lectures on Polytopes},
	SERIES = {Graduate texts in Mathematics},
	PUBLISHER = {Springer-Verlag},
	ADDRESS = {New York},
	VOLUME = {152},
	YEAR = {1998},
	PAGES = {vii+370},
}

@book {Matousek,
	AUTHOR = {Matou{\v{s}}ek, Ji{\v{r}}{\'{\i}}},
	TITLE = {Lectures on discrete geometry},
	SERIES = {Graduate Texts in Mathematics},
	VOLUME = {212},
	PUBLISHER = {Springer-Verlag, New York},
	YEAR = {2002},
	PAGES = {xvi+481},
}

@book {Bourbaki,
	AUTHOR = {Nicolas Bourbaki},
	TITLE = {{G}roupes et alg\`ebres de {L}ie, {C}hapitres {IV--VI}},
	PAGES = {288 pp. (loose errata)},
	PUBLISHER = {Hermann},
	ADDRESS = {Paris},
	SERIES = {Actualit\'es Scientifiques et Industrielles, No. 1337},
	YEAR = {1968}
}

@book {Humphreys,
	AUTHOR = {James~E.~Humphreys},
	TITLE = {Reflection groups and {C}oxeter groups},
	SERIES = {Cambridge Studies in Advanced Mathematics},
	VOLUME = {29},
	PUBLISHER = {Cambridge University Press},
	ADDRESS = {Cambridge},
	YEAR = {1990},
	PAGES = {xii+204}
}

@book {Humphreys1978,
	AUTHOR = {James~E.~Humphreys},
	TITLE = {Introduction to {L}ie algebras and representation theory},
	SERIES = {Graduate Texts in Mathematics},
	VOLUME = {9},
	NOTE = {Second printing, revised},
	PUBLISHER = {Springer-Verlag},
	ADDRESS = {New York},
	YEAR = {1978},
	PAGES = {xii+171}
}

@book {BjornerBrenti,
	AUTHOR = {Bj{\"o}rner, Anders and Brenti, Francesco},
	TITLE = {Combinatorics of {C}oxeter groups},
    SERIES = {Graduate Texts in Mathematics},
	VOLUME = {231},
	PUBLISHER = {Springer, New York},
	YEAR = {2005},
	PAGES = {xiv+363},
}

@book {AssemSimsonSkowronski,
	AUTHOR = {Assem, Ibrahim and Simson, Daniel and Skowro\'nski, Andrzej},
	TITLE = {Elements of the representation theory of associative algebras. {V}ol. 1},
	SERIES = {London Mathematical Society Student Texts},
	VOLUME = {65},
	NOTE = {Techniques of representation theory},
	PUBLISHER = {Cambridge University Press, Cambridge},
	YEAR = {2006},
	PAGES = {x+458},
}

@book {Schiffler,
	AUTHOR = {Schiffler, Ralf},
	TITLE = {Quiver representations},
	SERIES = {CMS Books in Mathematics/Ouvrages de Math\'ematiques de la SMC},
	PUBLISHER = {Springer, Cham},
	YEAR = {2014},
	PAGES = {xii+230},
}

@book {FlajoletSedgewick,
	AUTHOR = {Flajolet, Philippe and Sedgewick, Robert},
	TITLE = {Analytic combinatorics},
	PUBLISHER = {Cambridge University Press, Cambridge},
	YEAR = {2009},
	PAGES = {xiv+810},
}

@book {BjornerLasVergnasSturmfelsWhiteZiegler,
	AUTHOR = {Anders~Bj{\"o}rner and Michel~{Las Vergnas} and Bernd~Sturmfels and Neil~White and G{\"u}nter~M.~Ziegler},
	TITLE = {Oriented matroids},
	SERIES = {Encyclopedia of Mathematics and its Applications},
	VOLUME = {46},
	EDITION = {Second},
	PUBLISHER = {Cambridge University Press},
	ADDRESS = {Cambridge},
	YEAR = {1999},
	PAGES = {xii+548},
}

@book {Bokowski,
    AUTHOR = {J{\"u}rgen~Bokowski},
	TITLE = {Computational oriented matroids},
	PUBLISHER = {Cambridge University Press},
	ADDRESS = {Cambridge},
	YEAR = {2006},
	PAGES = {xiv+323},
}

@book {Stanley,
	AUTHOR = {Stanley, Richard P.},
	TITLE = {Enumerative combinatorics. {V}ol. 2},
	SERIES = {Cambridge Studies in Advanced Mathematics},
	VOLUME = {62},
	NOTE = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin},
	PUBLISHER = {Cambridge University Press, Cambridge},
	YEAR = {1999},
	PAGES = {xii+581},
}

% associahedron

@phdthesis{Tamari,
	AUTHOR = {Dov Tamari},
	TITLE = {Monoides pr\'eordonn\'es et cha\^ines de Malcev},
	SCHOOL = {Universit\'e Paris Sorbonne},
	YEAR = {1951},
}

@article {HuangTamari,
	AUTHOR = {Huang, Samuel and Tamari, Dov},
	TITLE = {Problems of associativity: {A} simple proof for the lattice property of systems ordered by a semi-associative law},
	JOURNAL = {J. Combinatorial Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A},
	VOLUME = {13},
	YEAR = {1972},
	PAGES = {7--13},
}

@article {Stasheff,
	AUTHOR = {Jim~Stasheff},
	TITLE = {Homotopy associativity of {H}-spaces {I}, {II}},
	JOURNAL = {Trans. Amer. Math. Soc.},
	FJOURNAL = {Transactions of the Americcan Mathematical Society},
	VOLUME = {108},
	YEAR = {1963},
	NUMBER = {2},
	PAGES = {293--312},
}

@inproceedings {StasheffShnider,
	AUTHOR = {Jim~Stasheff},
	TITLE = {From operads to ``physically'' inspired theories},
	BOOKTITLE = {Operads: Proceedings of Renaissance Conferences (Hartfort, CT/Luminy, 1995)},
	SERIES = {Contemporary Mathematics},
	VOLUME = {202},
	PUBLISHER = {American Mathematical Society},
	ADDRESS = {Cambridge, MA},
	YEAR = {1997},
	PAGES = {53--81},
	NOTE = {Appendix~B by Steve Shnider and Jim~Stasheff for a corrected polytope construction}
}

@book {ShniderSternberg,
	AUTHOR = {Steve~Shnider and Shlomo~Sternberg},
	TITLE = {Quantum groups: From coalgebras to {D}rinfeld algebras},
	SERIES = {Series in Mathematical Physics},
	PUBLISHER = {International Press},
	ADDRESS = {Cambridge, MA},
	YEAR = {1993},
	PAGES = {592},
}

@unpublished {Haiman,
	AUTHOR = {Mark Haiman},
	TITLE = {Constructing the associahedron},
 	NOTE = {Unpublished manuscript, 11 pages, available at \url{http://www.math.berkeley.edu/~mhaiman/ftp/assoc/manuscript.pdf}}, 
	YEAR = {1984},
}

@article {Lee,
	AUTHOR = {Carl~W.~Lee},
	TITLE = {The associahedron and triangulations of the {$n$}-gon},
	JOURNAL = {European J.~Combin.},
	FJOURNAL = {European Journal of Combinatorics},
	VOLUME = {10},
	YEAR = {1989},
	NUMBER = {6},
	PAGES = {551--560},
}

@book {GelfandKapranovZelevinsky,
	AUTHOR = {Israel~Gelfand and Mikhail~Kapranov and Andrei~Zelevinsky},
	TITLE = {Discriminants, resultants and multidimensional determinants},
	SERIES = {Modern Birkh\"auser Classics},
	NOTE = {Reprint of the 1994 edition},
	PUBLISHER = {Birkh\"auser Boston Inc.},
	ADDRESS = {Boston, MA},
	YEAR = {2008},
	PAGES = {x+523},
}

@article {BilleraFillimanSturmfels,
	AUTHOR = {Louis~J.~Billera and Paul~Filliman and Bernd~Sturmfels},
	TITLE = {Constructions and complexity of secondary polytopes},
	JOURNAL = {Adv.~Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {83},
	YEAR = {1990},
	NUMBER = {2},
	PAGES = {155--179},
}

@article {Loday,
	AUTHOR = {Jean-Louis~Loday},
	TITLE = {Realization of the {S}tasheff polytope},
	JOURNAL = {Arch.~Math.~(Basel)},
	FJOURNAL = {Archiv der Mathematik},
	VOLUME = {83},
	YEAR = {2004},
	NUMBER = {3},
	PAGES = {267--278},
}

@article {HohlwegLange,
	AUTHOR = {Christophe~Hohlweg and Carsten~Lange},
	TITLE = {Realizations of the associahedron and cyclohedron},
	JOURNAL = {Discrete Comput.~Geom.},
	FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	VOLUME = {37},
	YEAR = {2007},
	NUMBER = {4},
	PAGES = {517--543}
}

@article {Lange,
	AUTHOR = {Carsten E. M.~C.~Lange},
	TITLE = {Minkowski Decomposition of Associahedra and Related Combinatorics},
	JOURNAL = {Discrete Comput.~Geom.},
	FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	YEAR = {2013},
	VOLUME = {50},
	NUMBER = {4},
	PAGES = {903--939},
}

@article {LangePilaud,
	AUTHOR = {Lange, Carsten and Pilaud, Vincent},
	TITLE = {Associahedra via spines},
	JOURNAL = {Combinatorica},
	FJOURNAL = {Combinatorica. An International Journal on Combinatorics and the Theory of Computing},
	VOLUME = {38},
	YEAR = {2018},
	NUMBER = {2},
	PAGES = {443--486},
}

@article {PilaudSantos-brickPolytope,
	AUTHOR = {Vincent~Pilaud and Francisco~Santos},
	TITLE = {The brick polytope of a sorting network},
	JOURNAL = {European~J.~Combin.},
	FJOURNAL = {European Journal of Combinatorics},
	VOLUME = {33},
	YEAR = {2012},
	NUMBER = {4},
	PAGES = {632--662},
}

@article {CeballosSantosZiegler,
	AUTHOR = {Cesar~Ceballos and Francisco~Santos and G\"unter~M.~Ziegler},
	TITLE = {Many non-equivalent realizations of the associahedron},
	JOURNAL = {Combinatorica},
	YEAR = {2015},
	VOLUME = {35},
	NUMBER = {5},
	PAGES = {513--551},
}

@book {TamariFestschrift,
	TITLE = {Associahedra, {T}amari Lattices and Related Structures. Tamari Memorial Festschrift},
	EDITOR = {Folkert M{\"u}ller-Hoissen and Jean Marcel Pallo and Jim Stasheff},
	PUBLISHER = {Springer},
	ADDRESS = {New York},
	SERIES = {Progress in Mathematics},
	VOLUME = {299},
	YEAR = {2012},
	PAGES = {xx+433},
}

@article {SleatorTarjanThurston,
	AUTHOR = {Daniel D. Sleator and Robert E. Tarjan and William P. Thurston},
	TITLE = {Rotation distance, triangulations, and hyperbolic geometry},
	JOURNAL = {J. Amer. Math. Soc.},
	FJOURNAL = {Journal of the American Mathematical Society},
	VOLUME = {1},
	YEAR = {1988},
	NUMBER = {3},
	PAGES = {647--681},
}

@article {Dehornoy,
	AUTHOR = {Dehornoy, Patrick},
	TITLE = {On the rotation distance between binary trees},
	JOURNAL = {Adv. Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {223},
	YEAR = {2010},
	NUMBER = {4},
	PAGES = {1316--1355},
}

@article {Trotter,
	AUTHOR = {Trotter, H. F.},
	TITLE = {Algorithm 115: Perm},
	JOURNAL = {Commun. ACM},
	VOLUME = {5},
	NUMBER = {8},
	YEAR = {1962},
	PAGES = {434--435},
} 

@book {Steinhaus,
	AUTHOR = {Steinhaus, Hugo},
	TITLE = {One hundred problems in elementary mathematics},
	PUBLISHER = {Basic Books Inc. Publishers},
	ADDRESS = {New York},
	YEAR = {1964},
	PAGES = {174},
}

@article {Johnson,
	AUTHOR = {Johnson, Selmer M.},
	TITLE = {Generation of permutations by adjacent transposition},
	JOURNAL = {Math. Comp.},
	FJOURNAL = {Mathematics of Computation},
	VOLUME = {17},
	YEAR = {1963},
	PAGES = {282--285},
}

@article {Pournin,
	AUTHOR = {Lionel Pournin},
	TITLE = {The diameter of associahedra},
	JOURNAL = {Adv. Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {259},
	YEAR = {2014},
	PAGES = {13--42},
}

@article {Pournin-diameterTypeB,
	AUTHOR = {Lionel Pournin},
	TITLE = {The asymptotic diameter of cyclohedra},
	JOURNAL = {Israel J. Math.},
	FJOURNAL = {Israel Journal of Mathematics},
	VOLUME = {219},
	YEAR = {2017},
	NUMBER = {2},
	PAGES = {609--635}
}

@article {Lucas,
	AUTHOR = {Lucas, Joan M.},
	TITLE = {The rotation graph of binary trees is {H}amiltonian},
	JOURNAL = {J. Algorithms},
	FJOURNAL = {Journal of Algorithms},
	VOLUME = {8},
	YEAR = {1987},
	NUMBER = {4},
	PAGES = {503--535},
}

@article {HurtadoNoy,
	AUTHOR = {Ferran Hurtado and Marc Noy},
	TITLE = {Graph of triangulations of a convex polygon and tree of triangulations},
	JOURNAL = {Comput. Geom.},
	FJOURNAL = {Computational Geometry. Theory and Applications},
	VOLUME = {13},
	YEAR = {1999},
	NUMBER = {3},
	PAGES = {179--188},
}

@book {Narayana,
	AUTHOR = {Tadepalli V.~Narayana},
	TITLE = {Lattice path combinatorics with statistical applications},
	SERIES = {Mathematical Expositions},
	VOLUME = {23},
	PUBLISHER = {University of Toronto Press},
	ADDRESS = {Toronto, Ont.},
	YEAR = {1979},
	PAGES = {xii+106},
}

@article {PilaudSantos-multitriangulations,
	AUTHOR = {Pilaud, Vincent and Santos, Francisco},
	TITLE = {Multitriangulations as complexes of star polygons},
	JOURNAL = {Discrete Comput. Geom.},
	FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	VOLUME = {41},
	YEAR = {2009},
	NUMBER = {2},
	PAGES = {284--317},
}

@incollection {RoteSantosStreinu-pseudotriangulations,
	AUTHOR = {Rote, G\"{u}nter and Santos, Francisco and Streinu, Ileana},
	TITLE = {Pseudo-triangulations---a survey},
	BOOKTITLE = {Surveys on discrete and computational geometry},
	SERIES = {Contemp. Math.},
	VOLUME = {453},
	PAGES = {343--410},
	PUBLISHER = {Amer. Math. Soc., Providence, RI},
	YEAR = {2008},
}

@incollection {RoteSantosStreinu-polytope,
	AUTHOR = {G{\"u}nter~Rote and Francisco~Santos and Ileana~Streinu},
	TITLE = {Expansive motions and the polytope of pointed pseudo-triangulations},
	BOOKTITLE = {Discrete and computational geometry},
	SERIES = {Algorithms Combin.},
	VOLUME = {25},
	PAGES = {699--736},
	PUBLISHER = {Springer},
	ADDRESS = {Berlin},
	YEAR = {2003},
}

@article {PocchiolaVegter,
	AUTHOR = {Michel~Pocchiola and Gert~Vegter},
	TITLE = {Topologically sweeping visibility complexes via pseudotriangulations},
	JOURNAL = {Discrete Comput.~Geom.},
	FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	VOLUME = {16},
	YEAR = {1996},
	NUMBER = {4},
	PAGES = {419--453},
}

@article {CeballosPadrolSarmiento-geometryNuTamari,
	AUTHOR = {Ceballos, Cesar and Padrol, Arnau and Sarmiento, Camilo},
	TITLE = {Geometry of {$\nu$}-{T}amari lattices in types {$A$} and {$B$}},
	JOURNAL = {Trans. Amer. Math. Soc.},
	FJOURNAL = {Transactions of the American Mathematical Society},
	VOLUME = {371},
	YEAR = {2019},
	NUMBER = {4},
	PAGES = {2575--2622},
}

@article {BergeronPrevilleRatelle,
	AUTHOR = {Bergeron, Fran\ced{c}ois and Pr\'eville-Ratelle, Louis-Fran\ced{c}ois},
	TITLE = {Higher trivariate diagonal harmonics via generalized {Tamari} posets},
	JOURNAL = {Journal of Combinatorics},
	VOLUME = {3},
	NUMBER = {3},
	YEAR = {2012},
	PAGES = {317--341},
}

@article {PrevilleRatelleViennot,
	AUTHOR = {Pr\'eville-Ratelle, Louis-Fran\ced{c}ois and Viennot, Xavier},
	TITLE = {The enumeration of generalized {T}amari intervals},
	JOURNAL = {Trans. Amer. Math. Soc.},
	FJOURNAL = {Transactions of the American Mathematical Society},
	VOLUME = {369},
	YEAR = {2017},
	NUMBER = {7},
	PAGES = {5219--5239},
}

@article {Bergeron-multivariateDiagonalCoinvariantSpaces,
	AUTHOR = {Bergeron, Fran\ced{c}ois},
	TITLE = {Multivariate diagonal coinvariant spaces for complex reflection groups},
	JOURNAL = {Adv. Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {239},
	YEAR = {2013},
	PAGES = {97--108},
}

@incollection {Street,
	AUTHOR = {Ross Street},
	TITLE = {Parenthetic Remarks},
	BOOKTITLE = {Associahedra, {T}amari lattices and related structures},
	SERIES = {Prog. Math. Phys.},
	VOLUME = {299},
	PAGES = {251--268},
	PUBLISHER = {Birkh\"auser/Springer, Basel},
	YEAR = {2012},
}

@unpublished {MasudaThomasTonksVallette,
	AUTHOR = {Naruki Masuda and Hugh Thomas and Andy Tonks and Bruno Vallette},
	TITLE = {The diagonal of the associahedra},
	NOTE = {\href{https://arxiv.org/abs/1902.08059}{\texttt{arXiv:1902.08059}}},
	YEAR = {2019},
}

@article {Keller-AinfinityAlgebras,
	AUTHOR = {Bernhard Keller},
	TITLE = {Introduction to $A$-infinity algebras and modules},
	JOURNAL = {Homology Homotopy Appl.},
	FJOURNAL = {Homology, Homotopy and Applications},
	VOLUME = {3},
	YEAR = {2001},
	NUMBER = {1},
	PAGES = {1--35.},
}

% grid associahedra, accordion complexes, gentle associahedra

@incollection {Baryshnikov,
	AUTHOR = {Baryshnikov, Yuliy},
	TITLE = {On {S}tokes sets},
	BOOKTITLE = {New developments in singularity theory ({C}ambridge, 2000)},
	SERIES = {NATO Sci. Ser. II Math. Phys. Chem.},
	VOLUME = {21},
	PAGES = {65--86},
	PUBLISHER = {Kluwer Acad. Publ., Dordrecht},
	YEAR = {2001},
}

@article {Chapoton-quadrangulations,
	AUTHOR = {Fr\'ed\'eric Chapoton},
	TITLE = {Stokes posets and serpent nests},
	JOURNAL = {Discrete Math. Theor. Comput. Sci.},
	VOLUME = {18},
	NUMBER = {3},
	YEAR = {2016},
}

@article {GarverMcConville-OrientedExchangeGraphs,
   	AUTHOR = {Alexander Garver and Thomas McConville},
	TITLE = {Lattice Properties of Oriented Exchange Graphs and Torsion Classes},
	JOURNAL = {Algebr. Represent. Theory},
	FJOURNAL = {Algebras and Representation Theory},
	YEAR = {2017},
}

@article {GarverMcConville,
    AUTHOR = {Garver, Alexander and McConville, Thomas},
	TITLE = {Oriented flip graphs of polygonal subdivisions and noncrossing tree partitions},
	JOURNAL = {J. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A},
	VOLUME = {158},
	YEAR = {2018},
	PAGES = {126--175},
}

@article {MannevillePilaud-accordion,
	AUTHOR = {Thibault Manneville and Vincent Pilaud},
	TITLE = {Geometric realizations of the accordion complex of a dissection},
	JOURNAL = {Discrete Comput. Geom.},
	FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	VOLUME = {61},
	YEAR = {2019},
	NUMBER = {3},
	PAGES = {507--540},
}

@article {PilaudPlamondonStella,
	AUTHOR = {Pilaud, Vincent and Plamondon, Pierre-Guy and Stella, Salvatore},
	TITLE = {A {$\tau$}-tilting approach to dissections of polygons},
	JOURNAL = {SIGMA Symmetry Integrability Geom. Methods Appl.},
	FJOURNAL = {SIGMA. Symmetry, Integrability and Geometry. Methods and Applications},
	VOLUME = {14},
	YEAR = {2018},
	PAGES = {Paper No. 045, 8},
}


@article {PetersenPylyavskyySpeyer,
	AUTHOR = {Petersen, T. Kyle and Pylyavskyy, Pavlo and Speyer, David E.},
	TITLE = {A non-crossing standard monomial theory},
	JOURNAL = {J. Algebra},
	FJOURNAL = {Journal of Algebra},
	VOLUME = {324},
	YEAR = {2010},
	NUMBER = {5},
	PAGES = {951--969},
}

@article {SantosStumpWelker,
	AUTHOR = {Santos, Francisco and Stump, Christian and Welker, Volkmar},
	TITLE = {Noncrossing sets and a {G}rassmann associahedron},
	JOURNAL = {Forum Math. Sigma},
	FJOURNAL = {Forum of Mathematics. Sigma},
	VOLUME = {5},
	YEAR = {2017},
	PAGES = {e5, 49},
}

@article {McConville,
	AUTHOR = {Thomas McConville},
	TITLE = {Lattice structure of {G}rid-{T}amari orders},
	JOURNAL = {J. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory, Series A},
	VOLUME = {148},
	YEAR = {2017},
	PAGES = {27--56},
}

@unpublished {GarverMcConville-grid,
	AUTHOR = {Alexander Garver and Thomas McConville},
	TITLE = {Enumerative properties of {G}rid-{A}ssociahedra},
 	NOTE = {\href{https://arxiv.org/abs/1705.04901}{\texttt{arXiv:1705.04901}}}, 
	YEAR = {2017},
}

@unpublished {PaluPilaudPlamondon-nonkissing,
	AUTHOR = {Yann Palu and Vincent Pilaud and Pierre-Guy Plamondon},
	TITLE = {Non-kissing complexes and tau-tilting for gentle algebras},
 	NOTE = {\href{https://arxiv.org/abs/1707.07574}{\texttt{arXiv:1707.07574}}. To appear in \emph{Mem. Amer. Math. Soc.}}, 
	YEAR = {2017},
}

@article {PaluPilaudPlamondon-surfaces,
	AUTHOR = {Palu, Yann and Pilaud, Vincent and Plamondon, Pierre-Guy},
	TITLE = {Non-kissing and non-crossing complexes for locally gentle algebras},
	JOURNAL = {J. Comb. Algebra},
	FJOURNAL = {Journal of Combinatorial Algebra},
	VOLUME = {3},
	YEAR = {2019},
	NUMBER = {4},
	PAGES = {401--438},
}

@unpublished {BanerjeeLaddhaRaman,
	AUTHOR = {Pinaki Banerjee and Alok Laddha and Prashanth Raman},
	TITLE = {Stokes Polytopes : The positive geometry for $\phi^4$ interactions},
 	NOTE = {\href{https://arxiv.org/abs/1811.05904}{\texttt{arXiv:1811.05904}}}, 
	YEAR = {2018},
}

@unpublished {Raman,
	AUTHOR = {Prashanth Raman},
	TITLE = {The positive geometry for $\phi^p$ interactions},
 	NOTE = {\href{https://arxiv.org/abs/1906.02985}{\texttt{arXiv:1906.02985}}}, 
	YEAR = {2019},
}

@unpublished {Chhatoi,
	AUTHOR = {Saroj Chhatoi},
	TITLE = {A Note on Convex Realization of Halohedron},
 	NOTE = {\href{https://arxiv.org/abs/1910.13786}{\texttt{arXiv:1910.13786}}}, 
	YEAR = {2019},
}

@unpublished {JagadaleKalyanapuramBalakrishnan,
	AUTHOR = {Mrunmay Jagadale and Nikhil Kalyanapuram and Aneesh Prema Balakrishnan},
	TITLE = {Accordiohedra as Positive Geometries for Generic Scalar Field Theories},
 	NOTE = {\href{https://arxiv.org/abs/1906.12148}{\texttt{arXiv:1906.12148}}}, 
	YEAR = {2019},
}

@unpublished {Kalyanapuram,
	AUTHOR = {Nikhil Kalyanapuram},
	TITLE = {Stokes Polytopes and Intersection Theory},
 	NOTE = {\href{https://arxiv.org/abs/1910.12195}{\texttt{arXiv:1910.12195}}}, 
	YEAR = {2019},
}

@unpublished {AneeshBanerjeeJagadaleJohnLaddhaMahato,
	AUTHOR = {P B Aneesh and Pinaki Banerjee and Mrunmay Jagadale and Renjan Rajan John and Alok Laddha and Sujoy Mahato},
	TITLE = {On Positive Geometries of Quartic Interactions II : Stokes polytopes, Lower Forms on Associahedra and Worldsheet Forms},
 	NOTE = {\href{https://arxiv.org/abs/1911.06008}{\texttt{arXiv:1911.06008}}}, 
	YEAR = {2019},
}

% cluster algebras, generalized associahedra

@unpublished {Fomin,
	AUTHOR = {Sergey Fomin},
	TITLE = {Cluster Algebras Portal},
	NOTE = {\url{http://www.math.lsa.umich.edu/~fomin/cluster.html}},
}

@article {FominZelevinsky-YSystems,
	AUTHOR = {Sergey Fomin and Andrei Zelevinsky},
	TITLE = {{$Y$}-systems and generalized associahedra},
	JOURNAL = {Ann. of Math. (2)},
	FJOURNAL = {Annals of Mathematics. Second Series},
	VOLUME = {158},
	YEAR = {2003},
	NUMBER = {3},
	PAGES = {977--1018},
}

@article {FominZelevinsky-ClusterAlgebrasI,
	AUTHOR = {Sergey Fomin and Andrei Zelevinsky},
	TITLE = {Cluster algebras. {I}. {F}oundations},
	JOURNAL = {J. Amer. Math. Soc.},
	FJOURNAL = {Journal of the American Mathematical Society},
	VOLUME = {15},
	YEAR = {2002},
	NUMBER = {2},
	PAGES = {497--529},
}

@article {FominZelevinsky-ClusterAlgebrasII,
	AUTHOR = {Sergey Fomin and Andrei Zelevinsky},
	TITLE = {Cluster algebras. {II}. {F}inite type classification},
	JOURNAL = {Invent. Math.},
	FJOURNAL = {Inventiones Mathematicae},
	VOLUME = {154},
	YEAR = {2003},
	NUMBER = {1},
	PAGES = {63--121},
}

@article {FominZelevinsky-ClusterAlgebrasIII,
	AUTHOR = {Sergey Fomin and Andrei Zelevinsky},
	TITLE = {Cluster algebras. {III}. {U}pper bounds and double {B}ruhat cells},
	JOURNAL = {Duke Math. J.},
	FJOURNAL = {Duke Mathematical Journal},
	VOLUME = {126},
	YEAR = {2005},
	NUMBER = {1},
	PAGES = {1--52},
}

@article {FominZelevinsky-ClusterAlgebrasIV,
	AUTHOR = {Sergey Fomin and Andrei Zelevinsky},
	TITLE = {Cluster algebras. {IV}. {C}oefficients},
	JOURNAL = {Compos. Math.},
	FJOURNAL = {Compositio Mathematica},
	VOLUME = {143},
	YEAR = {2007},
	NUMBER = {1},
	PAGES = {112--164},
}

@incollection {NakanishiZelevinsky,
	AUTHOR = {Nakanishi, Tomoki and Zelevinsky, Andrei},
	TITLE = {On tropical dualities in cluster algebras},
	BOOKTITLE = {Algebraic groups and quantum groups},
	SERIES = {Contemp. Math.},
	VOLUME = {565},
	PAGES = {217--226},
	PUBLISHER = {Amer. Math. Soc., Providence, RI},
	YEAR = {2012},
}

@article {NakanishiStella,
	AUTHOR = {Nakanishi, Tomoki and Stella, Salvatore},
	TITLE = {Diagrammatic description of {$c$}-vectors and {$d$}-vectors of cluster algebras of finite type},
	JOURNAL = {Electron. J. Combin.},
	FJOURNAL = {Electronic Journal of Combinatorics},
	VOLUME = {21},
	YEAR = {2014},
	NUMBER = {1},
	PAGES = {Paper 1.3, 107},
}

@article {YangZelevinsky,
	AUTHOR = {Yang, Shih-Wei and Zelevinsky, Andrei},
	TITLE = {Cluster algebras of finite type via {C}oxeter elements and principal minors},
	JOURNAL = {Transform. Groups},
	FJOURNAL = {Transformation Groups},
	VOLUME = {13},
	YEAR = {2008},
	NUMBER = {3-4},
	PAGES = {855--895},
}

@article {FominShapiroThurston,
	AUTHOR = {Fomin, Sergey and Shapiro, Michael and Thurston, Dylan},
	TITLE = {Cluster algebras and triangulated surfaces {I}. {C}luster complexes},
	JOURNAL = {Acta Math.},
	FJOURNAL = {Acta Mathematica},
	VOLUME = {201},
	YEAR = {2008},
	NUMBER = {1},
	PAGES = {83--146},
}

@article {FominThurston,
	AUTHOR = {Sergey Fomin and Dylan Thurston},
	TITLE = {Cluster algebras and triangulated surfaces. {P}art {II}: {L}ambda lengths},
	JOURNAL = {Mem. Amer. Math. Soc.},
	FJOURNAL = {Memoirs of the American Mathematical Society},
	VOLUME = {255},
	YEAR = {2018},
	NUMBER = {1223},
	PAGES = {v+97},
}

@article {MusikerSchifflerWilliams,
	AUTHOR = {Musiker, Gregg and Schiffler, Ralf and Williams, Lauren},
	TITLE = {Positivity for cluster algebras from surfaces},
	JOURNAL = {Adv. Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {227},
	YEAR = {2011},
	NUMBER = {6},
	PAGES = {2241--2308},
}

@article {LamPylyavskyy-LaurentPhenomenonAlgebras,
	AUTHOR = {Thomas Lam and Pavlo Pylyavskyy},
	TITLE = {{L}aurent phenomenon algebras},
	JOURNAL = {Camb. J. Math.},
	FJOURNAL = {Cambridge Journal of Mathematics},
	VOLUME = {4},
	YEAR = {2016},
	NUMBER = {1},
	PAGES = {121--162},
}

@article {LamPylyavskyy-LinearLaurentPhenomenonAlgebras,
	AUTHOR = {Thomas Lam and Pavlo Pylyavskyy},
	TITLE = {Linear {L}aurent phenomenon algebras},
	JOURNAL = {Int. Math. Res. Not. IMRN},
	FJOURNAL = {International Mathematics Research Notices. IMRN},
	YEAR = {2016},
	NUMBER = {10},
	PAGES = {3163--3203},
}

@article {ChapotonFominZelevinsky,
	AUTHOR = {Fr{\'e}d{\'e}ric~Chapoton and Sergey~Fomin and Andrei~Zelevinsky},
	TITLE = {Polytopal Realizations of Generalized Associahedra},
	JOURNAL = {Canad. Math. Bull.},
	FJOURNAL = {Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques. },
	VOLUME = {45},
	YEAR = {2002},
	NUMBER = {4},
	PAGES = {537--566},
}

@article {HohlwegLangeThomas,
	AUTHOR = {Christophe~Hohlweg and Carsten~Lange and Hugh~Thomas},
	TITLE = {Permutahedra and generalized associahedra},
	JOURNAL = {Adv. Math.},
	FJOURNAL = {Adances in Mathematics},
	VOLUME = {226},
	YEAR = {2011},
	NUMBER = {1},
	PAGES = {608--640},
}

@article {Stella,
	AUTHOR = {Salvatore~Stella},
	TITLE = {Polyhedral models for generalized associahedra via {C}oxeter elements},
	JOURNAL = {J. Algebraic Combin.},
	FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
	VOLUME = {38},
	YEAR = {2013},
	NUMBER = {1},
	PAGES = {121--158},
}

@article {PilaudStump-brickPolytope,
	AUTHOR = {Vincent Pilaud and Christian Stump},
	TITLE = {Brick polytopes of spherical subword complexes and generalized associahedra},
	FJOURNAL = {Advances in Mathematics},
	JOURNAL = {Adv. Math.},
	PAGES = {1--61},
	VOLUME = {276},
	YEAR = {2015},
}

@article {HohlwegPilaudStella,
	AUTHOR = {Christophe Hohlweg and Vincent Pilaud and Salvatore Stella},
	TITLE = {Polytopal realizations of finite type $\mathbf{g}$-vector fans},
	FJOURNAL = {Advances in Mathematics},
	JOURNAL = {Adv. Math.},
	PAGES = {713--749},
	VOLUME = {328},
	YEAR = {2018},
}

@article {HohlwegLortieRaymond,
	AUTHOR = {Christophe~Hohlweg and Jonathan~Lortie and Annie~Raymond},
	TITLE = {The centers of gravity of the associahedron and of the permutahedron are the same},
	JOURNAL = {Electron. J. Combin.},
	FJOURNAL = {Electronic Journal of Combinatorics},
	VOLUME = {17},
	YEAR = {2010},
	NUMBER = {1},
	PAGES = {Research Paper 72, 14},
}

@article {PilaudStump-barycenter,
	AUTHOR = {Pilaud, Vincent and Stump, Christian},
	TITLE = {Vertex barycenter of generalized associahedra},
	JOURNAL = {Proc. Amer. Math. Soc.},
	FJOURNAL = {Proceedings of the American Mathematical Society},
	VOLUME = {143},
	YEAR = {2015},
    NUMBER = {6},
	PAGES = {2623--2636},
}

@article {BergeronHohlwegLangeThomas,
	AUTHOR = {Nantel Bergeron and Christophe Hohlweg and Carsten Lange and Hugh Thomas},
	TITLE = {Isometry classes of generalized associahedra},
	JOURNAL = {S\'em. Lothar. Combin.},
	FJOURNAL = {S\'eminaire Lotharingien de Combinatoire},
	VOLUME = {61A},
	YEAR = {2009},
	PAGES = {Art. B61Aa, 13},
}

@incollection {Hohlweg,
	AUTHOR = {Hohlweg, Christophe},
	TITLE = {Permutahedra and associahedra: generalized associahedra from the geometry of finite reflection groups},
	BOOKTITLE = {Associahedra, {T}amari lattices and related structures},
	SERIES = {Prog. Math. Phys.},
	VOLUME = {299},
	PAGES = {129--159},
	PUBLISHER = {Birkh\"auser/Springer, Basel},
	YEAR = {2012},
}

@article {CeballosPilaud-diameterDAssociahedron,
	AUTHOR = {Ceballos, Cesar and Pilaud, Vincent},
	TITLE = {The diameter of type {$D$} associahedra and the non-leaving-face property},
	JOURNAL = {European J. Combin.},
	FJOURNAL = {European Journal of Combinatorics},
	VOLUME = {51},
	YEAR = {2016},
	PAGES = {109--124},
}

@article {Williams-nonLeavingFaceProperty,
	AUTHOR = {Williams, Nathan},
	TITLE = {{$W$}-associahedra have the non-leaving-face property},
	JOURNAL = {European J. Combin.},
	FJOURNAL = {European Journal of Combinatorics},
	VOLUME = {62},
	YEAR = {2017},
	PAGES = {272--285},
}

@unpublished {HoangMutze,
	AUTHOR = {Hung P. Hoang and Torsten M{\"u}tze},
	TITLE = {Combinatorial generation via permutation languages. II. Lattice congruences},
	NOTE = {\href{https://arxiv.org/abs/1911.12078}{\texttt{arXiv:1911.12078}}},
	YEAR = {2019},
}

@article {CeballosPilaud-pseudotriangulationsTypeD,
	AUTHOR = {Ceballos, Cesar and Pilaud, Vincent},
	TITLE = {Cluster algebras of type {$D$}: pseudotriangulations approach},
	JOURNAL = {Electron. J. Combin.},
	FJOURNAL = {Electronic Journal of Combinatorics},
	VOLUME = {22},
	YEAR = {2015},
	NUMBER = {4},
	PAGES = {Paper 4.44, 27},
}

@article {Reading-UniversalCoefficients,
	AUTHOR = {Reading, Nathan},
	TITLE = {Universal geometric cluster algebras},
	JOURNAL = {Math. Z.},
	FJOURNAL = {Mathematische Zeitschrift},
	VOLUME = {277},
	YEAR = {2014},
	NUMBER = {1-2},
	PAGES = {499--547},
}

@incollection {Keller,
	AUTHOR = {Keller, Bernhard},
	TITLE = {On cluster theory and quantum dilogarithm identities},
	BOOKTITLE = {Representations of algebras and related topics},
	SERIES = {EMS Ser. Congr. Rep.},
	PAGES = {85--116},
	PUBLISHER = {Eur. Math. Soc., Z\"urich},
	YEAR = {2011},
}

% scattering diagrams

@article {GrossHackingKeelKontsevich,
	AUTHOR = {Gross, Mark and Hacking, Paul and Keel, Sean and Kontsevich, Maxim},
	TITLE = {Canonical bases for cluster algebras},
	JOURNAL = {J. Amer. Math. Soc.},
	FJOURNAL = {Journal of the American Mathematical Society},
	VOLUME = {31},
	YEAR = {2018},
	NUMBER = {2},
	PAGES = {497--608},
}

@unpublished {Reading-scatteringFans,
	AUTHOR = {Nathan Reading},
	TITLE = {Scattering fans},
 	NOTE = {\href{https://arxiv.org/abs/1712.06968}{\texttt{arXiv:1712.06968}}}, 
	YEAR = {2017},
}

% lattice quotients, Cambrian lattices

@article {Edelman,
	AUTHOR = {Edelman, Paul H.},
	TITLE = {A partial order on the regions of~$\mathbb{R}^n$ dissected by hyperplanes},
	JOURNAL = {Trans. Amer. Math. Soc.},
	FJOURNAL = {Transactions of the Americcan Mathematical Society},
	VOLUME = {283},
	YEAR = {1984},
	PAGES = {617--631},
}

@article {Reading-posetRegions,
	AUTHOR = {Reading, Nathan},
	TITLE = {Lattice and order properties of the poset of regions in a hyperplane arrangement},
	JOURNAL = {Algebra Universalis},
	FJOURNAL = {Algebra Universalis},
	VOLUME = {50},
	YEAR = {2003},
	NUMBER = {2},
	PAGES = {179--205},
}

@article {BjornerEdelmanZiegler,
	AUTHOR = {Bj\"orner, Anders and Edelman, Paul H. and Ziegler, G\"unter M.},
	TITLE = {Hyperplane arrangements with a lattice of regions},
	JOURNAL = {Discrete Comput. Geom.},
	FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	VOLUME = {5},
	YEAR = {1990},
	NUMBER = {3},
	PAGES = {263--288},
}

@article {Reading-HyperplaneArrangement,
	AUTHOR = {Reading, Nathan},
	TITLE = {Lattice and order properties of the poset of regions in a hyperplane arrangement},
	JOURNAL = {Algebra Universalis},
	FJOURNAL = {Algebra Universalis},
	VOLUME = {50},
	YEAR = {2003},
	NUMBER = {2},
	PAGES = {179--205},
}

@article {Reading-shardIntersectionOrder,
	AUTHOR = {Reading, Nathan},
	TITLE = {Noncrossing partitions and the shard intersection order},
	JOURNAL = {J. Algebraic Combin.},
	FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
	VOLUME = {33},
	YEAR = {2011},
	NUMBER = {4},
	PAGES = {483--530},
}

@article {Reading-latticeCongruences,
	AUTHOR = {Nathan~Reading},
	TITLE = {Lattice congruences of the weak order},
	JOURNAL = {Order},
	FJOURNAL = {Order. A Journal on the Theory of Ordered Sets and its Applications},
	VOLUME = {21},
	YEAR = {2004},
	NUMBER = {4},
	PAGES = {315--344},
}

@article {Reading-cambrianLattices,
	AUTHOR = {Nathan~Reading},
	TITLE = {Cambrian lattices},
	JOURNAL = {Adv.~Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {205},
	YEAR = {2006},
	NUMBER = {2},
	PAGES = {313--353},
}

@article {Reading-coxeterSortable,
	AUTHOR = {Nathan~Reading},
	TITLE = {Clusters, {C}oxeter-sortable elements and noncrossing partitions},
	JOURNAL = {Trans. Amer. Math. Soc.},
	FJOURNAL = {Transactions of the American Mathematical Society},
	VOLUME = {359},
	YEAR = {2007},
	NUMBER = {12},
	PAGES = {5931--5958}
}

@article {Reading-sortableElements,
	AUTHOR = {Nathan~Reading},
	TITLE = {Sortable elements and {C}ambrian lattices},
	JOURNAL = {Algebra Universalis},
	FJOURNAL = {Algebra Universalis},
	VOLUME = {56},
	YEAR = {2007},
	NUMBER = {3-4},
	PAGES = {411--437},
}

@article {ReadingSpeyer,
	AUTHOR = {Nathan~Reading and David~E.~Speyer},
	TITLE = {Cambrian fans},
	JOURNAL = {J.~Eur.~Math.~Soc.},
	FJOURNAL = {Journal of the European Mathematical Society (JEMS)},
	VOLUME = {11},
	YEAR = {2009},
	NUMBER = {2},
	PAGES = {407--447}
}

@article {Reading-arcDiagrams,
	AUTHOR = {Reading, Nathan},
	TITLE = {Noncrossing arc diagrams and canonical join representations},
	JOURNAL = {SIAM J. Discrete Math.},
	FJOURNAL = {SIAM Journal on Discrete Mathematics},
	VOLUME = {29},
	YEAR = {2015},
	NUMBER = {2},
	PAGES = {736--750},
}

@incollection{Reading-survey,
	Author = {Nathan Reading},
	Booktitle = {Associahedra, Tamari Lattices and Related Structures~--~Tamari Memorial Festschrift},
	Editor = {Folkert~M{\"u}ller-Hoissen and Jean~Pallo and Jim~Stasheff},
	Pages = {293--322},
	Publisher = {Birkh{\"a}user},
	Series = {Progress in Mathematics},
	Title = {From the Tamari Lattice to Cambrian Lattices and Beyond},
	Volume = {299},
	Year = {2012}
}

@incollection {Reading-FiniteCoxeterGroupsChapter,
	AUTHOR = {Reading, Nathan},
	TITLE = {Finite {C}oxeter groups and the weak order},
	BOOKTITLE = {Lattice theory: special topics and applications. {V}ol. 2},
	PAGES = {489--561},
	PUBLISHER = {Birkh\"auser/Springer, Cham},
	YEAR = {2016},
}	

@incollection {Reading-PosetRegionsChapter,
	AUTHOR = {Reading, Nathan},
	TITLE = {Lattice theory of the poset of regions},
	BOOKTITLE = {Lattice theory: special topics and applications. {V}ol. 2},
	PAGES = {399--487},
	PUBLISHER = {Birkh\"auser/Springer, Cham},
	YEAR = {2016},
}

@article {FreeseNation,
    AUTHOR = {Ralph Freese and J. B. Nation},
    TITLE = {Free lattices},
    JOURNAL = {Mathematical Surveys and Monographs},
    YEAR = {1995},
    VOLUME = {75},
    PAGES = {93--106}
}

@article {PilaudSantos-quotientopes,
	AUTHOR = {Vincent Pilaud and Francisco Santos},
	TITLE = {Quotientopes},
    JOURNAL = {Bull. Lond. Math. Soc.},
	FJOURNAL = {Bulletin of the London Mathematical Society},
    YEAR = {2019},
    VOLUME = {51},
    NUMBER = {3},
    PAGES = {406--420}
}

@unpublished {PadrolPilaudRitter,
	AUTHOR = {Arnau Padrol and Vincent Pilaud and Julian Ritter},
	TITLE = {Quotientopes via Minkowski sums of shard polytopes},
    YEAR = {2020},
    NOTE = {In preparation}
}

% Hopf algebras

@article {MalvenutoReutenauer,
	AUTHOR = {Malvenuto, Claudia and Reutenauer, Christophe},
	TITLE = {Duality between quasi-symmetric functions and the {S}olomon descent algebra},
	JOURNAL = {J. Algebra},
	FJOURNAL = {Journal of Algebra},
	VOLUME = {177},
	YEAR = {1995},
	NUMBER = {3},
	PAGES = {967--982},
}

@article {NovelliThibon-coloredHopfAlgebras,
	AUTHOR = {Novelli, Jean-Christophe and Thibon, Jean-Yves},
	TITLE = {Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions},
	JOURNAL = {Discrete Math.},
	FJOURNAL = {Discrete Mathematics},
	VOLUME = {310},
	YEAR = {2010},
	NUMBER = {24},
	PAGES = {3584--3606},
}

@article {Solomon,
	AUTHOR = {Solomon, Louis},
	TITLE = {A {M}ackey formula in the group ring of a {C}oxeter group},
	JOURNAL = {J. Algebra},
	FJOURNAL = {Journal of Algebra},
	VOLUME = {41},
	YEAR = {1976},
	NUMBER = {2},
	PAGES = {255--264},
}

@article {GelfandKrobLascouxLeclercRetakhThibon,
	AUTHOR = {Gelfand, Israel M. and Krob, Daniel and Lascoux, Alain and Leclerc, Bernard and Retakh, Vladimir S. and Thibon, Jean-Yves},
	TITLE = {Noncommutative symmetric functions},
	JOURNAL = {Adv. Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {112},
	YEAR = {1995},
	NUMBER = {2},
	PAGES = {218--348},
}

@article {LodayRonco,
	AUTHOR = {Loday, Jean-Louis and Ronco, Mar{\'{\i}}a O.},
	TITLE = {Hopf algebra of the planar binary trees},
	JOURNAL = {Adv. Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {139},
	YEAR = {1998},
	NUMBER = {2},
	PAGES = {293--309},
}

@article {HivertNovelliThibon-algebraBinarySearchTrees,
	AUTHOR = {Hivert, Florent and Novelli, Jean-Christophe and Thibon, Jean-Yves},
	TITLE = {The algebra of binary search trees},
	JOURNAL = {Theoret. Comput. Sci.},
	FJOURNAL = {Theoretical Computer Science},
	VOLUME = {339},
	YEAR = {2005},
	NUMBER = {1},
	PAGES = {129--165},
}

@article {Chapoton,
	AUTHOR = {Chapoton, Fr{\'e}d{\'e}ric},
	TITLE = {Alg\`ebres de {H}opf des permutah\`edres, associah\`edres et hypercubes},
	JOURNAL = {Adv. Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {150},
	YEAR = {2000},
	NUMBER = {2},
	PAGES = {264--275},
}

@article {Reading-HopfAlgebras,
	AUTHOR = {Reading, Nathan},
	TITLE = {Lattice congruences, fans and {H}opf algebras},
	JOURNAL = {J. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A},
	VOLUME = {110},
	YEAR = {2005},
	NUMBER = {2},
	PAGES = {237--273},
}

@article {Giraudo,
	AUTHOR = {Giraudo, Samuele},
	TITLE = {Algebraic and combinatorial structures on pairs of twin binary trees},
	JOURNAL = {J. Algebra},
	FJOURNAL = {Journal of Algebra},
	VOLUME = {360},
	YEAR = {2012},
	PAGES = {115--157},
}

@article {LawReading,
	AUTHOR = {Law, Shirley and Reading, Nathan},
	TITLE = {The {H}opf algebra of diagonal rectangulations},
	JOURNAL = {J. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A},
	VOLUME = {119},
	YEAR = {2012},
	NUMBER = {3},
	PAGES = {788--824},
}

@article {ChatelPilaud,
	AUTHOR = {Gr\'egory Chatel and Vincent Pilaud},
	TITLE = {{C}ambrian {H}opf {Algebras}},
	JOURNAL = {Adv. Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {311},
	YEAR = {2017},
	PAGES = {598--633},
}

@article{NovelliReutenauerThibon,
	AUTHOR = {Novelli, Jean-Christophe and Reutenauer, Christophe and Thibon, Jean-Yves},
	TITLE = {Generalized descent patterns in permutations and associated {H}opf algebras},
	JOURNAL = {European J. Combin.},
	FJOURNAL = {European Journal of Combinatorics},
	VOLUME = {32},
	YEAR = {2011},
	NUMBER = {4},
	PAGES = {618--627},
}

@article {PilaudPons-permutrees,
    AUTHOR = {Pilaud, Vincent and Pons, Viviane},
    TITLE = {Permutrees},
	JOURNAL = {Algebraic Combinatorics},
	PUBLISHER = {MathOA foundation},
	VOLUME = {1},
	NUMBER = {2},
	YEAR = {2018},
	PAGES = {173--224},
}

@misc {PilaudPonsTamayo,
	AUTHOR = {Vincent Pilaud and Viviane Pons and Daniel Tamayo Jim\'enez},
	TITLE = {Permutree sorting},
    EPRINT = {2007.07802},
    EPRINTTYPE = {arXiv},
	YEAR = {2020},
}


@article {Pilaud-brickAlgebra,
	AUTHOR = {Vincent Pilaud},
	TITLE = {Brick polytopes, lattice quotients, and {H}opf algebras},
	JOURNAL = {J. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A},
	VOLUME = {155},
	YEAR = {2018},
	PAGES = {418--457},
}

@inproceedings {PilaudPons-HopfAlgebraRelations,
	AUTHOR = {Vincent Pilaud and Viviane Pons},
	TITLE = {The {H}opf algebra of integer binary relations},
	BOOKTITLE = {Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA)},
	SERIES = {IRMA Lectures in Mathematics and Theoretical Physics},
	VOLUME = {31},
	PAGES = {299--344},
	PUBLISHER = {Europ. Math. Soc.},
	YEAR = {2020},
}

@unpublished {BergeronCeballosPilaud,
	AUTHOR = {Nantel Bergeron and Cesar Ceballos and Vincent Pilaud},
	TITLE = {Hopf dreams},
 	NOTE = {\href{https://arxiv.org/abs/1807.03044}{\texttt{arXiv:1807.03044}}}, 
	YEAR = {2018},
}

@unpublished {Law,
	AUTHOR = {Shirley Law},
	TITLE = {Combinatorial Realization of the {H}opf Algebra of Sashes},
 	NOTE = {\href{https://arxiv.org/abs/1407.4073}{\texttt{arXiv:1407.4073}}}, 
	YEAR = {2014},
}

@article {Pilaud-arcDiagramAlgebra,
	AUTHOR = {Pilaud, Vincent},
	TITLE = {Hopf algebras on decorated noncrossing arc diagrams},
	JOURNAL = {J. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A},
	VOLUME = {161},
	YEAR = {2019},
	PAGES = {486--507},
}

@unpublished {AguiarArdila,
	AUTHOR = {Marcelo Aguiar and Federico Ardila},
	TITLE = {Hopf monoids and generalized permutahedra},
 	NOTE = {\href{https://arxiv.org/abs/1709.07504}{\texttt{arXiv:1709.07504}}}, 
	YEAR = {2017},
}

@article {AguiarSottile-MalvenutoReutenauerHopfAlgebra,
	AUTHOR = {Aguiar, Marcelo and Sottile, Frank},
	TITLE = {Structure of the {M}alvenuto-{R}eutenauer {H}opf algebra of permutations},
	JOURNAL = {Adv. Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {191},
	YEAR = {2005},
	NUMBER = {2},
	PAGES = {225--275},
}

@article{AguiarSottile-LodayRoncoHopfAlgebra,
	AUTHOR = {Aguiar, Marcelo and Sottile, Frank},
	TITLE = {Structure of the {L}oday-{R}onco {H}opf algebra of trees},
	JOURNAL = {J. Algebra},
	FJOURNAL = {Journal of Algebra},
	NUMBER = {2},
	PAGES = {473--511},
	VOLUME = {295},
	YEAR = {2006}
}

@incollection {Viennot,
	AUTHOR = {Xavier Viennot},
	TITLE = {Catalan tableaux and the asymmetric exclusion process},
	BOOKTITLE = {19th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2007)},
	YEAR = {2007},
}

@article {NovelliThibon-decoratedFQSym,
	AUTHOR = {Novelli, Jean-Christophe and Thibon, Jean-Yves},
	TITLE = {Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions},
	JOURNAL = {Discrete Math.},
	FJOURNAL = {Discrete Mathematics},
	VOLUME = {310},
	YEAR = {2010},
	NUMBER = {24},
	PAGES = {3584--3606},
}

@article {Novelli-hypoplactic,
	AUTHOR = {Novelli, Jean-Christophe},
	TITLE = {On the hypoplactic monoid},
	NOTE = {Formal power series and algebraic combinatorics (Vienna, 1997)},
	JOURNAL = {Discrete Math.},
	FJOURNAL = {Discrete Mathematics},
	VOLUME = {217},
	YEAR = {2000},
	NUMBER = {1-3},
	PAGES = {315--336},
}

@article {KrobThibon-NCSF4,
	AUTHOR = {Krob, Daniel and Thibon, Jean-Yves},
	TITLE = {Noncommutative symmetric functions. {IV}. {Q}uantum linear groups and {H}ecke algebras at {$q=0$}},
	JOURNAL = {J. Algebraic Combin.},
	FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
	VOLUME = {6},
	YEAR = {1997},
	NUMBER = {4},
	PAGES = {339--376},
}

@unpublished{NovelliThibon-trialgebras,
	AUTHOR = {Jean-Christophe Novelli and Jean-Yves Thibon},
	NOTE = {18th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2006)},
	TITLE = {Polynomial realizations of some trialgebras},
	YEAR = {2006}
}

@article {NovelliThibon-trigebres,
	AUTHOR = {Novelli, Jean-Christophe and Thibon, Jean-Yves},
	TITLE = {Construction de trig\`ebres dendriformes},
	JOURNAL = {C. R. Math. Acad. Sci. Paris},
	FJOURNAL = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris},
	VOLUME = {342},
	YEAR = {2006},
	NUMBER = {6},
	PAGES = {365--369},
}

@article {BergeronZabrocki,
	AUTHOR = {Bergeron, Nantel and Zabrocki, Mike},
	TITLE = {The {H}opf algebras of symmetric functions and quasi-symmetric functions in non-commutative variables are free and co-free},
	JOURNAL = {J. Algebra Appl.},
	FJOURNAL = {Journal of Algebra and its Applications},
	VOLUME = {8},
	YEAR = {2009},
	NUMBER = {4},
	PAGES = {581--600},
}

@unpublished {HivertPilaud-signaleticOperads,
	AUTHOR = {Florent Hivert and Vincent Pilaud},
	TITLE = {Signaletic operads},
 	NOTE = {\href{https://arxiv.org/abs/1906.02228}{\texttt{arXiv:1906.02228}}}, 
	YEAR = {2019},
}

@article{KasselLascouxReutenauer,
	AUTHOR = {Christian Kassel and Alain Lascoux and Christophe Reutenauer},
	TITLE = {The singular locus of a {S}chubert variety},
	FJOURNAL = {Journal of Algebra},
	JOURNAL = {J. Algebra},
	NUMBER = {1},
	PAGES = {74--108},
	VOLUME = {269},
	YEAR = {2003}
}

% nestohedra

@article {Postnikov,
	AUTHOR = {Alexander~Postnikov},
	TITLE = {Permutohedra, associahedra, and beyond},
	JOURNAL = {Int. Math. Res. Not. IMRN},
	FJOURNAL = {International Mathematics Research Notices. IMRN},
	YEAR = {2009},
	NUMBER = {6},
	PAGES = {1026--1106},
}

@article {PostnikovReinerWilliams,
	AUTHOR = {Alexander~Postnikov and Victor~Reiner and Lauren K. Williams},
	TITLE = {Faces of generalized permutohedra},
	JOURNAL = {Doc.~Math.},
	FJOURNAL = {Documenta Mathematica},
	VOLUME = {13},
	YEAR = {2008},
	PAGES = {207--273},
}

@article {ArdilaBenedettiDoker,
	AUTHOR = {Federico~Ardila and Carolina~Benedetti and Jeffrey~Doker},
	TITLE = {Matroid polytopes and their volumes},
	JOURNAL = {Discrete Comput.~Geom.},
	FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	VOLUME = {43},
	YEAR = {2010},
	NUMBER = {4},
	PAGES = {841--854},
}

@article {FeichtnerSturmfels,
	AUTHOR = {Eva~Maria~Feichtner and Bernd~Sturmfels},
	TITLE = {Matroid polytopes, nested sets and {B}ergman fans},
	JOURNAL = {Port. Math. (N.S.)},
	FJOURNAL = {Portugaliae Mathematica. Nova S\'erie},
	VOLUME = {62},
	YEAR = {2005},
	NUMBER = {4},
	PAGES = {437--468},
}

@article {Zelevinsky,
	AUTHOR = {Andrei Zelevinsky},
	TITLE = {Nested complexes and their polyhedral realizations},
	JOURNAL = {Pure Appl. Math. Q.},
	FJOURNAL = {Pure and Applied Mathematics Quarterly},
	VOLUME = {2},
	YEAR = {2006},
	NUMBER = {3},
	PAGES = {655--671},
}

@article {CarrDevadoss,
	AUTHOR = {Michael~P.~Carr and Satyan~L.~Devadoss},
	TITLE = {Coxeter complexes and graph-associahedra},
	JOURNAL = {Topology Appl.},
	FJOURNAL = {Topology and its Applications},
	VOLUME = {153},
	YEAR = {2006},
	NUMBER = {12},
	PAGES = {2155--2168},
}

@article {Devadoss,
	AUTHOR = {Satyan L. Devadoss},
	TITLE = {A realization of graph associahedra},
	JOURNAL = {Discrete Math.},
	FJOURNAL = {Discrete Mathematics},
	VOLUME = {309},
	YEAR = {2009},
	NUMBER = {1},
	PAGES = {271--276},
}

@unpublished {Pilaud-signedTreeAssociahedra,
	AUTHOR = {Vincent Pilaud},
	TITLE = {Signed tree associahedra},
 	NOTE = {\href{https://arxiv.org/abs/1309.5222}{\texttt{arXiv:1309.5222}}}, 
	YEAR = {2013},
}

@article {MannevillePilaud-graphPropertiesGraphAssociahedra,
	AUTHOR = {Thibault Manneville and Vincent Pilaud},
	TITLE = {Graph properties of graph associahedra},
	JOURNAL = {S\'em. Lothar. Combin.},
	FJOURNAL = {S\'eminaire Lotharingien de Combinatoire},
	PAGES = {Art. B73d, 31\,pp},
	YEAR = {2015},
}

@article {MannevillePilaud-compatibilityFans,
	AUTHOR = {Manneville, Thibault and Pilaud, Vincent},
	TITLE = {Compatibility fans for graphical nested complexes},
	JOURNAL = {J. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A},
	VOLUME = {150},
	YEAR = {2017},
	PAGES = {36--107},
}

@article {Pilaud-removahedra,
	AUTHOR = {Pilaud, Vincent},
	TITLE = {Which nestohedra are removahedra?},
	JOURNAL = {Rev. Colombiana Mat.},
	FJOURNAL = {Revista Colombiana de Matem\'aticas},
	VOLUME = {51},
	YEAR = {2017},
	NUMBER = {1},
	PAGES = {21--42},
}

@article {HuberRambauSantos,
	AUTHOR = {Huber, Birkett and Rambau, J\"org and Santos, Francisco},
	TITLE = {The {C}ayley trick, lifting subdivisions and the {B}ohne-{D}ress theorem on zonotopal tilings},
	JOURNAL = {J. Eur. Math. Soc. (JEMS)},
	FJOURNAL = {Journal of the European Mathematical Society (JEMS)},
	VOLUME = {2},
	YEAR = {2000},
	NUMBER = {2},
	PAGES = {179--198},
}

@article {DevelinSturmfels,
	AUTHOR = {Develin, Mike and Sturmfels, Bernd},
	TITLE = {Tropical convexity},
	JOURNAL = {Doc. Math.},
	FJOURNAL = {Documenta Mathematica},
	VOLUME = {9},
	YEAR = {2004},
	PAGES = {1--27},
}

@article {DeConciniProcesi,
	AUTHOR = {De Concini, Conrado and Procesi, Claudio},
	TITLE = {Wonderful models of subspace arrangements},
	JOURNAL = {Selecta Math. (N.S.)},
	FJOURNAL = {Selecta Mathematica. New Series},
	VOLUME = {1},
	YEAR = {1995},
	NUMBER = {3},
	PAGES = {459--494},
}

% subword complex

@article {KnutsonMiller-subwordComplex,
	AUTHOR = {Allen~Knutson and Ezra~Miller},
	TITLE = {Subword complexes in {C}oxeter groups},
	JOURNAL = {Adv.~Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {184},
	YEAR = {2004},
	NUMBER = {1},
	PAGES = {161--176}
}

@article {KnutsonMiller-GroebnerGeometry,
	AUTHOR = {Allen~Knutson and Ezra~Miller},
	TITLE = {Gr\"obner geometry of {S}chubert polynomials},
	JOURNAL = {Ann. of Math. (2)},
	FJOURNAL = {Annals of Mathematics. Second Series},
	VOLUME = {161},
	YEAR = {2005},
	NUMBER = {3},
	PAGES = {1245--1318}
}

@article{BergeronBilley,
	AUTHOR = {Bergeron, Nantel and Billey, Sara},
	TITLE = {R{C}-graphs and {S}chubert polynomials},
	FJOURNAL = {Experimental Mathematics},
	JOURNAL = {Experiment. Math.},
	NUMBER = {4},
	PAGES = {257--269},
	VOLUME = {2},
	YEAR = {1993}
}

@unpublished {Woo,
	AUTHOR = {A.~Woo},
	TITLE = {Catalan numbers and {S}chubert polynomials for $w=1(n+1)... 2$},
 	NOTE = {\href{https://arxiv.org/abs/math/0407160}{\texttt{arXiv:math/0407160}}}, 
	YEAR = {2004},
}

@article {PilaudPocchiola,
	AUTHOR = {Vincent Pilaud and Michel Pocchiola},
	TITLE = {Multitriangulations, pseudotriangulations and primitive sorting networks},
	JOURNAL = {Discrete Comput. Geom.},
	FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	VOLUME = {48},
	YEAR = {2012},
	NUMBER = {1},
	PAGES = {142--191},
}

@article {Stump,
	AUTHOR = {Christian~Stump},
	TITLE = {A new perspective on $k$-triangulations},
	JOURNAL = {J. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A },
	VOLUME = {118},
	YEAR = {2011},
	NUMBER = {6},
	PAGES = {1794--1800},
}

@article {SerranoStump,
	AUTHOR = {Luis~Serrano and Christian~Stump},
	TITLE = {Maximal fillings of moon polyominoes, simplicial complexes, and {S}chubert polynomials},
	JOURNAL = {Electron. J. Combin.},
	FJOURNAL = {Electronic Journal Combinatorics},
	VOLUME = {19},
	YEAR = {2012},
}

@article {CeballosLabbeStump,
	AUTHOR = {Cesar~Ceballos and Jean-Philippe~Labb\'e and Christian~Stump},
	TITLE = {Subword complexes, cluster complexes, and generalized multi-associahedra},
	JOURNAL = {J. Algebraic Combin.},
	FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
	VOLUME = {39},
	YEAR = {2014},
	NUMBER = {1},
	PAGES = {17--51},
}

@incollection {PilaudStump-ELlabeling,
	AUTHOR = {Vincent Pilaud and Christian Stump},
	TITLE = {{EL}-labelings and canonical spanning trees for subword complexes},
	BOOKTITLE = {Discrete Geometry and Optimization},
	PUBLISHER = {Springer},
	SERIES = {Fields Institute Communications Series},
	YEAR = {2013},
	PAGES = {213--248},
}

@article {CeballosPilaud,
	AUTHOR = {Cesar Ceballos and Vincent Pilaud},
	TITLE = {Denominator vectors and compatibility degrees in cluster algebras of finite types},
 	JOURNAL = {Trans. Amer. Math. Soc.},
	FJOURNAL = {Transactions of the Americcan Mathematical Society},
	VOLUME = {367},
	PAGES = {1421--1439},
	YEAR = {2015},
}

% generalizations weak order

@incollection{Bjorner,
	AUTHOR = {Bj{\"o}rner, Anders},
	TITLE = {Orderings of {C}oxeter groups},
	BOOKTITLE = {Combinatorics and algebra ({B}oulder, {C}olo., 1983)},
	PAGES = {175--195},
	PUBLISHER = {Amer. Math. Soc., Providence, RI},
	SERIES = {Contemp. Math.},
	VOLUME = {34},
	YEAR = {1984}
}

@article{BjornerWachs,
	AUTHOR = {Bj{\"o}rner, Anders and Wachs, Michelle L.},
	TITLE = {Permutation statistics and linear extensions of posets},
	JOURNAL = {J. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A},
	NUMBER = {1},
	PAGES = {85--114},
	VOLUME = {58},
	YEAR = {1991}
}

@unpublished {KrobLatapyNovelliPhanSchwer,
	AUTHOR = {Daniel Krob and Matthieu Latapy and Jean-Christophe Novelli and Ha-Duong Phan and Sylviane Schwer},
	TITLE = {Pseudo-{P}ermutations {I}: {F}irst {C}ombinatorial and {L}attice {P}roperties},
	NOTE = {13th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2001)},
	YEAR = {2001},
}

@incollection {BoulierHivertKrobNovelli,
	AUTHOR = {Boulier, Fran\ced{c}ois and Hivert, Florent and Krob, Daniel and Novelli, Jean-Christophe},
	TITLE = {Pseudo-permutations. {II}. {G}eometry and representation theory},
	BOOKTITLE = {Discrete models: combinatorics, computation, and geometry ({P}aris, 2001)},
	SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AA},
	PAGES = {123--132 (electronic)},
	PUBLISHER = {Maison Inform. Math. Discr\`et. (MIMD), Paris},
	YEAR = {2001},
}

@article {PalaciosRonco,
	AUTHOR = {Palacios, Patricia and Ronco, Mar{\'{\i}}a O.},
	TITLE = {Weak {B}ruhat order on the set of faces of the permutohedron and the associahedron},
	JOURNAL = {J. Algebra},
	FJOURNAL = {Journal of Algebra},
	VOLUME = {299},
	YEAR = {2006},
	NUMBER = {2},
	PAGES = {648--678},
}

@article {DermenjianHohlwegPilaud,
	AUTHOR = {Aram Dermenjian and Christophe Hohlweg and Vincent Pilaud},
	TITLE = {The facial weak order and its lattice quotients},
	JOURNAL = {Trans. Amer. Math. Soc.},
	FJOURNAL = {Transactions of the American Mathematical Society},
	VOLUME = {370},
	YEAR = {2018},
	NUMBER = {2},
	PAGES = {1469--1507},
}

@article{McMullen,
	AUTHOR = {Peter {McMullen}},
	TITLE = {On zonotopes},
	FJOURNAL = {Transactions of the American Mathematical Society},
	JOURNAL = {Trans. Amer. Math. Soc.},
	PAGES = {91--109},
	VOLUME = {159},
	YEAR = {1971}
}

@unpublished {DermenjianHohlwegMcConvillePilaud,
	AUTHOR = {Aram Dermenjian and Christophe Hohlweg and Thomas McConville and Vincent Pilaud},
	TITLE = {The facial weak order on hyperplane arrangements},
	NOTE = {\href{https://arxiv.org/abs/1910.03511}{\texttt{arXiv:1910.03511}}},
	YEAR = {2019},
}

@article {ChatelPilaudPons,
    AUTHOR = {Chatel, Gr\'egory and Pilaud, Vincent and Pons, Viviane},
    TITLE = {The weak order on integer posets},
	JOURNAL = {Algebraic Combinatorics},
	PUBLISHER = {MathOA foundation},
	VOLUME = {2},
	NUMBER = {1},
	YEAR = {2019},
	PAGES = {1--48},
}

@article {Pilkington,
	AUTHOR = {Pilkington, Annette},
	TITLE = {Convex geometries on root systems},
	JOURNAL = {Comm. Algebra},
	FJOURNAL = {Communications in Algebra},
	VOLUME = {34},
	YEAR = {2006},
	NUMBER = {9},
	PAGES = {3183--3202},
}

@unpublished {GayPilaud,
	AUTHOR = {Jo\"el Gay and Vincent Pilaud},
	TITLE = {The weak order on Weyl posets},
	NOTE = {\href{https://arxiv.org/abs/1804.06572}{\texttt{arXiv:1804.06572}}. To appear in \href{https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/weak-order-on-weyl-posets/33AFC4F4F1DE4A94BA13974C71B74A6F}{\emph{Canad. J. Math.}}},
	YEAR = {2018},
}

% representation theory

@unpublished {DemonetIyamaReadingReitenThomas,
	AUTHOR = {Laurent Demonet and Osamu Iyama and Nathan Reading and Idun Reiten and Hugh Thomas},
	TITLE = {Lattice theory of torsion classes},
 	NOTE = {\href{https://arxiv.org/abs/1711.01785}{\texttt{arXiv:1711.01785}}}, 
	YEAR = {2017},
}

@article {DemonetIyamaJasso,
	AUTHOR = {Laurent Demonet and Osamu Iyama and Gustavo Jasso},
	TITLE = {$\tau$-tilting finite algebras, $\b{g}$-vectors and brick-$\tau$-rigid correspondence},
	JOURNAL = {Int. Math. Res. Not. IMRN},
	FJOURNAL = {International Mathematics Research Notices. IMRN},
	YEAR = {2017},
	PAGES = {Art. ID rnx135, 17},
}

@unpublished {BrustleDouvilleMousavandThomasYildirim,
	AUTHOR = {Thomas Br\"ustle and Guillaume Douville and Kaveh Mousavand and Hugh Thomas and Emine Y\i{}ld\i{}r\i{}m},
	TITLE = {On the combinatorics of gentle algebras},
 	NOTE = {\href{https://arxiv.org/abs/1707.07665}{\texttt{arXiv:1707.07665}}. To appear in \href{https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/on-the-combinatorics-of-gentle-algebras/DAC0E0FF011FBAC0FD9E45F473AE2E99}{\emph{Canad. J. Math.}}}, 
	YEAR = {2017},
}

@article {AdachiIyamaReiten,
	AUTHOR = {Adachi, Takahide and Iyama, Osamu and Reiten, Idun},
	TITLE = {{$\tau$}-tilting theory},
	JOURNAL = {Compos. Math.},
	FJOURNAL = {Compositio Mathematica},
	VOLUME = {150},
	YEAR = {2014},
	NUMBER = {3},
	PAGES = {415--452},
}

@article {BuanMarshReinekeReitenTodorov,
	AUTHOR = {Buan, Aslak Bakke and Marsh, Robert and Reineke, Markus and Reiten, Idun and Todorov, Gordana},
	TITLE = {Tilting theory and cluster combinatorics},
	JOURNAL = {Adv. Math.},
	FJOURNAL = {Advances in Mathematics},
	VOLUME = {204},
	YEAR = {2006},
	NUMBER = {2},
	PAGES = {572--618},
}

@article {CalderoChapotonSchiffler,
	AUTHOR = {Caldero, Philippe and Chapoton, Fr\'d\'ric and Schiffler, Ralf},
	TITLE = {Quivers with relations arising from clusters ({$A_n$} case)},
	JOURNAL = {Trans. Amer. Math. Soc.},
	FJOURNAL = {Transactions of the American Mathematical Society},
	VOLUME = {358},
	YEAR = {2006},
	NUMBER = {3},
	PAGES = {1347--1364},
}

@article {DehyKeller,
	AUTHOR = {Dehy, Raika and Keller, Bernhard},
	TITLE = {On the combinatorics of rigid objects in 2-{C}alabi-{Y}au categories},
	JOURNAL = {Int. Math. Res. Not. IMRN},
	FJOURNAL = {International Mathematics Research Notices. IMRN},
	YEAR = {2008},
	NUMBER = {11},
	PAGES = {Art. ID rnn029, 17},
}

@article {ButlerRingel,
	AUTHOR = {Butler, M. C. R. and Ringel, Claus Michael},
	TITLE = {Auslander-{R}eiten sequences with few middle terms and applications to string algebras},
	JOURNAL = {Comm. Algebra},
	FJOURNAL = {Communications in Algebra},
	VOLUME = {15},
	YEAR = {1987},
	NUMBER = {1-2},
	PAGES = {145--179},
}

@article {Crawley-Boevey,
	AUTHOR = {Crawley-Boevey, William},
	TITLE = {Classification of modules for infinite-dimensional string algebras},
	JOURNAL = {Trans. Amer. Math. Soc.},
	FJOURNAL = {Transactions of the American Mathematical Society},
	VOLUME = {370},
	YEAR = {2018},
	NUMBER = {5},
	PAGES = {3289--3313},
}

@unpublished{BaurCoelhoSimoes,
	AUTHOR = {Baur, Karin and Coelho Sim\~oes, Raquel},
	TITLE = {A geometric model for the module category of a gentle algebra},
	NOTE = {\href{https://arxiv.org/abs/1803.05802}{\texttt{arXiv:1803.05802}}}, 
	YEAR = {2018},
}

@unpublished {OpperPlamondonSchroll,
	AUTHOR = {Sebastian Opper and Pierre-Guy Plamondon and Sibylle Schroll},
	TITLE = {A geometric model for the derived category of gentle algebras},
 	NOTE = {\href{https://arxiv.org/abs/1801.09659}{\texttt{arXiv:1801.09659}}}, 
	YEAR = {2018},
}

@article {BessenrodtHolm,
	AUTHOR = {Bessenrodt, Christine and Holm, Thorsten},
	TITLE = {Weighted locally gentle quivers and {C}artan matrices},
	JOURNAL = {J. Pure and Appl. Algebra},
	FJOURNAL = {Communications in Algebra},
	VOLUME = {212},
	YEAR = {2008},
	PAGES = {204--221},
}

% type cone

@unpublished {BazierMatteDouvilleMousavandThomasYildirim,
	AUTHOR = {V\'eronique Bazier-Matte and Guillaume Douville and Kaveh Mousavand and Hugh Thomas and Emine Y\i{}ld\i{}r\i{}m},
	TITLE = {{ABHY} {A}ssociahedra and {N}ewton polytopes of ${F}$-polynomials for finite type cluster algebras},
 	NOTE = {\href{https://arxiv.org/abs/1808.09986}{\texttt{arXiv:1808.09986}}}, 
	YEAR = {2018},
}

@article {ArkaniHamedBaiHeYan,
	AUTHOR = {Arkani-Hamed, Nima and Bai, Yuntao and He, Song and Yan, Gongwang},
	TITLE = {Scattering forms and the positive geometry of kinematics, color and the worldsheet},
	JOURNAL = {J. High Energy Phys.},
	FJOURNAL = {Journal of High Energy Physics},
	YEAR = {2018},
	NUMBER = {5},
	PAGES = {096, front matter+75},
}

@article {McMullen-typeCone,
	AUTHOR = {McMullen, Peter},
	TITLE = {Representations of polytopes and polyhedral sets},
	JOURNAL = {Geometriae Dedicata},
	FJOURNAL = {Geometriae Dedicata},
	VOLUME = {2},
	YEAR = {1973},
	PAGES = {83--99},
}

@unpublished {PadrolPaluPilaudPlamondon,
	AUTHOR = {Arnau Padrol and Yann Palu and Vincent Pilaud and Pierre-Guy Plamondon},
	TITLE = {Associahedra for finite type cluster algebras and minimal relations between $\b{g}$-vectors},
 	NOTE = {\href{https://arxiv.org/abs/1906.06861}{\texttt{arXiv:1906.06861}}}, 
	YEAR = {2019},
}

@unpublished {ArdilaCastilloEurPostnikov,
	AUTHOR = {Federico Ardila and Federico Castillo and Christopher Eur and Alexander Postnikov},
	TITLE = {Coxeter submodular functions and deformations of Coxeter permutahedra},
 	NOTE = {\href{https://arxiv.org/abs/1904.11029}{\texttt{arXiv:1904.11029}}}, 
	YEAR = {2019},
}

% sage, OEIS

@manual {Sage,
	AUTHOR = {The {S}age developers},
	TITLE = {{S}age {M}athematics {S}oftware},
	NOTE = {\url{https://www.sagemath.org}},
	YEAR = {2016},
}

@manual {SageCombinat,
	AUTHOR = {The {S}age-{C}ombinat community},
	TITLE = {{S}age-{C}ombinat: enhancing {S}age as a toolbox for computer exploration in algebraic combinatorics},
	NOTE = {\url{http://wiki.sagemath.org/combinat}},
	YEAR = {2016},
}

@unpublished {OEIS,
  	KEY = {{OEIS}},
	TITLE = {The {O}n-{L}ine {E}ncyclopedia of {I}nteger {S}equences},
	NOTE = {Published electronically at \url{https://oeis.org}},
	YEAR = {2010},
}

% my other publications

@article {MatschkePfeiflePilaud,
	AUTHOR = {Benjamin Matschke and Julian Pfeifle and Vincent Pilaud},
	TITLE = {Prodsimplicial neighborly polytopes},
	JOURNAL = {Discrete Comput.~Geom.},
	FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	VOLUME = {46},
	YEAR = {2011},
	NUMBER = {1},
	PAGES = {100--131}
}

@article {PfeiflePilaudSantos,
	AUTHOR = {Julian Pfeifle and Vincent Pilaud and Francisco Santos},
	TITLE = {Polytopality and Cartesian products of graphs},
	JOURNAL = {Israel J. Math.},
	FJOURNAL = {Israel Journal of Mathematics},
	VOLUME = {192},
	YEAR = {2012},
	NUMBER = {1},
	PAGES = {121--141}
}

@article {HahnleKleePilaud,
	AUTHOR = {H\"ahnle, Nicolai and Klee, Steven and Pilaud, Vincent},
	TITLE = {Obstructions to weak decomposability for simplicial polytopes},
	JOURNAL = {Proc. Amer. Math. Soc.},
	FJOURNAL = {Proceedings of the American Mathematical Society},
	VOLUME = {142},
	YEAR = {2014},
	NUMBER = {9},
	PAGES = {3249--3257},
}

@article {BokowskiPilaud3,
	AUTHOR = {Bokowski, J\"urgen and Pilaud, Vincent},
	TITLE = {Quasi-configurations: building blocks for point-line configurations},
	JOURNAL = {Ars Math. Contemp.},
	FJOURNAL = {Ars Mathematica Contemporanea},
	VOLUME = {10},
	YEAR = {2016},
	NUMBER = {1},
	PAGES = {99--112},
}
		
@article {BokowskiPilaud2,
	AUTHOR = {Bokowski, J\"urgen and Pilaud, Vincent},
	TITLE = {On topological and geometric {$(19_4)$} configurations},
	JOURNAL = {European J. Combin.},
	FJOURNAL = {European Journal of Combinatorics},
	VOLUME = {50},
	YEAR = {2015},
	PAGES = {4--17},
}

@article {BokowskiPilaud1,
	AUTHOR = {Bokowski, J\"urgen and Pilaud, Vincent},
	TITLE = {Enumerating topological {$(n_k)$}-configurations},
	JOURNAL = {Comput. Geom.},
	FJOURNAL = {Computational Geometry. Theory and Applications},
	VOLUME = {47},
	YEAR = {2014},
	NUMBER = {2, part A},
	PAGES = {175--186},
}

@article {PilaudRue,
	AUTHOR = {Pilaud, Vincent and Ru\'e, Juanjo},
	TITLE = {Analytic combinatorics of chord and hyperchord diagrams with {$k$} crossings},
	JOURNAL = {Adv. in Appl. Math.},
	FJOURNAL = {Advances in Applied Mathematics},
	VOLUME = {57},
	YEAR = {2014},
	PAGES = {60--100},
}

@article {FertePilaudPocchiola,
	AUTHOR = {Julien Fert\'e and Vincent Pilaud and Michel Pocchiola},
	TITLE = {On the number of simple arrangements of five double pseudolines},
	JOURNAL = {Discrete Comput. Geom.},
	FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	VOLUME = {45},
	YEAR = {2011},
	NUMBER = {2},
	PAGES = {279--302},
}

% my conference papers

@incollection {BokowskiPilaud,
	AUTHOR = {J{\"u}rgen~G.~Bokowski and Vincent~Pilaud},
	TITLE = {On symmetric realizations of the simplicial complex of $3$-crossing-free sets of diagonals of the octagon},
	BOOKTITLE = {21st Canadian Conference on Comput.~Geom. (Vancouver)},
	YEAR = {2009},
}

@incollection {PilaudSantos-multitriangulationsFPSAC,
	AUTHOR = {Pilaud, Vincent and Santos, Francisco},
	TITLE = {Multi-triangulations as complexes of star polygons},
	BOOKTITLE = {20th {A}nnual {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2008)},
	SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AJ},
	PAGES = {319--330},
	PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
	YEAR = {2008},
}

@incollection {PilaudSantos-brickPolytopeFPSAC,
	AUTHOR = {Pilaud, Vincent and Santos, Francisco},
	TITLE = {The brick polytope of a sorting network},
	BOOKTITLE = {23rd {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2011)},
	SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AO},
	PAGES = {777--788},
	PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
	YEAR = {2011},
}
		
@incollection {PilaudStump-brickPolytopeFPSAC,
	AUTHOR = {Pilaud, Vincent and Christian Stump},
	TITLE = {Generalized associahedra via brick polytopes},
	BOOKTITLE = {24rd {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2012)},
	SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AO},
	PAGES = {73--84},
	PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
	YEAR = {2012},
}
		
@incollection {PilaudStump-ELlabelingFPSAC,
	AUTHOR = {Pilaud, Vincent and Stump, Christian},
	TITLE = {E{L}-labelings and canonical spanning trees for subword complexes},
	BOOKTITLE = {Discrete geometry and optimization},
	SERIES = {Fields Inst. Commun.},
	VOLUME = {69},
	PAGES = {213--248},
	PUBLISHER = {Springer, New York},
	YEAR = {2013},
}
		
@incollection {CeballosPilaud-denominatorsFPSAC,
	AUTHOR = {Ceballos, Cesar and Pilaud, Vincent},
	TITLE = {Denominator vectors and compatibility degrees in cluster algebras of finite type},
	BOOKTITLE = {25th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2013)},
	SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AS},
	PAGES = {85--96},
	PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
	YEAR = {2013},
}

@inproceedings {PilaudRue-AofA,
	AUTHOR = {Pilaud, Vincent and Ru\'e, Juanjo},
	TITLE = {Analytic combinatorics of chord and hyperchord diagrams with {$k$} crossings},
	BOOKTITLE = {Proceedings of the 25th {I}nternational {C}onference on {P}robabilistic, {C}ombinatorial and {A}symptotic {M}ethods for the {A}nalysis of {A}lgorithms},
	SERIES = {Discrete Math. Theor. Comput. Sci. Proc., BA},
	PAGES = {339--350},
	PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
	YEAR = {2014},
}

@incollection {Pilaud-signedTreeAssociahedraFPSAC,
	AUTHOR = {Pilaud, Vincent},
	TITLE = {Signed tree associahedra},
	BOOKTITLE = {26th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2014)},
	SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AS},
	PAGES = {309--320},
	PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
	YEAR = {2014},
}

@incollection {ChatelPilaud-FPSAC,
	AUTHOR = {Gr\'egory Chatel and Vincent Pilaud},
	TITLE = {The Cambrian Hopf Algebra},
	BOOKTITLE = {27th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2015)},
	SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AS},
	PAGES = {61--72},
	PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
	YEAR = {2015},
}

@incollection {CeballosMannevillePilaudPournin-FPSAC,
	AUTHOR = {Cesar Ceballos and Thibault Manneville and Vincent Pilaud and Lionel Pournin},
	TITLE = {Diameters and geodesic properties of generalizations of the associahedron},
	BOOKTITLE = {27th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2015)},
	SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AS},
	PAGES = {345--356},
	PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
	YEAR = {2015},
}

@incollection {DermenjianHohlwegPilaud-FPSAC,
	AUTHOR = {Aram Dermenjian and Christophe Hohlweg and Vincent Pilaud},
	TITLE = {The facial weak order in finite Coxeter groups},
	BOOKTITLE = {28th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2016)},
	SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AS},
	PAGES = {359--370},
	PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
	YEAR = {2016},
}

@incollection {MannevillePilaud-compatibilityFansFPSAC,
	AUTHOR = {Thibault Manneville and Vincent Pilaud},
	TITLE = {Compatibility fans realizing graphical nested complexes},
	BOOKTITLE = {28th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2016)},
	SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AS},
	PAGES = {827--838},
	PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
	YEAR = {2016},
}

@incollection {Pilaud-brickAlgebraFPSAC,
	AUTHOR = {Vincent Pilaud},
	TITLE = {Brick polytopes, lattices and Hopf algebras},
	BOOKTITLE = {28th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2016)},
	SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AS},
	PAGES = {1003--1014},
	PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
	YEAR = {2016},
}

@incollection {BateniMannevillePilaud-StokesComplexesFPSAC,
	AUTHOR = {Amir-Hossein Bateni and Thibault Manneville and Vincent Pilaud},
	TITLE = {On quadrangulations and Stokes complexes},
	NOTE = {The European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB'17)},
	JOURNAL = {Electronic Notes in Discrete Mathematics},
	PAGES = {107--113},
	VOLUME = {61},
	YEAR = {2017},
}

@incollection {PilaudPons-permutreesFPSAC,
	AUTHOR = {Vincent Pilaud and Viviane Pons},
	TITLE = {Permutrees},
	NOTE = {The European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB'17)},
	JOURNAL = {Electronic Notes in Discrete Mathematics},
	PAGES = {987--993},
	VOLUME = {61},
	YEAR = {2017},
}

@article {HohlwegPilaudStella-gvectorsFPSAC,
	AUTHOR = {Christophe Hohlweg and Vincent Pilaud and Salvatore Stella},
	TITLE = {Universal associahedra},
	BOOKTITLE = {30th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2018)},
	JOURNAL = {S\'em. Lothar. Combin.},
	FJOURNAL = {S\'eminaire Lotharingien de Combinatoire},
	PAGES = {Art. B80b, 15},
	YEAR = {2018},
}

@article {PaluPilaudPlamondon-nonkissingFPSAC,
	AUTHOR = {Yann Palu and Vincent Pilaud and Pierre-Guy Plamondon},
	TITLE = {Non-kissing complexes for gentle algebras},
	BOOKTITLE = {30th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2018)},
	JOURNAL = {S\'em. Lothar. Combin.},
	FJOURNAL = {S\'eminaire Lotharingien de Combinatoire},
	PAGES = {Art. B80b, 38},
	YEAR = {2018},
}

@article {PilaudPons-weakOrderPosetsFPSAC,
	AUTHOR = {Christophe Hohlweg and Vincent Pilaud and Salvatore Stella},
	TITLE = {Algebraic structures on integer posets},
	BOOKTITLE = {30th {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2018)},
	JOURNAL = {S\'em. Lothar. Combin.},
	FJOURNAL = {S\'eminaire Lotharingien de Combinatoire},
	PAGES = {Art. B80b, 61},
	YEAR = {2018},
}