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@article {bergeron_fan_2015,
    AUTHOR = {Bergeron, Nantel and Ceballos, Cesar and Labb\'{e}, Jean-Philippe},
     TITLE = {Fan realizations of type {$A$} subword complexes and
              multi-associahedra of rank 3},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {54},
      YEAR = {2015},
    NUMBER = {1},
     PAGES = {195--231},
      ISSN = {0179-5376},
       DOI = {10.1007/s00454-015-9691-0},
       URL = {https://doi.org/10.1007/s00454-015-9691-0},
}

\bibitem{steinitz_polyeder_1922}
E. Steinitz, “Polyeder und Raumeinteilungen”, in Encyklopa ̈die der mathematischen Wissenschaf-
ten, Anwendungen, Dritter Band: Geometrie, III.1.2., Heft 9, Kapitel IIIAB12, W. F. Meyer and H. Mohrmann, eds., B. G. Teubner, Leipzig, 1922, 1–139.

@article {hersh_sb_labelings_2017,
    AUTHOR = {Hersh, Patricia and M\'{e}sz\'{a}ros, Karola},
     TITLE = {{$SB$}-labelings and posets with each interval homotopy
              equivalent to a sphere or a ball},
   JOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {152},
      YEAR = {2017},
     PAGES = {104--120},
      ISSN = {0097-3165},
       DOI = {10.1016/j.jcta.2017.06.001},
       URL = {https://doi.org/10.1016/j.jcta.2017.06.001},
}

@misc{chapoton_personalCommunication_2021,
	author = {Fr{\'e}d{\'e}ric Chapoton},
	note = {Personal Communication},
	year = {2021},
}

@article {codenotti_relative_2019,
    AUTHOR = {Codenotti, Giulia and Katth\"{a}n, Lukas and Sanyal, Raman},
     TITLE = {On {$f$}- and {$h$}-vectors of relative simplicial complexes},
   JOURNAL = {Algebraic Combinatorics},
    VOLUME = {2},
      YEAR = {2019},
    NUMBER = {3},
     PAGES = {343--353},
}

@article {murai_face_2017,
    AUTHOR = {Murai, Satoshi and Novik, Isabella},
     TITLE = {Face numbers of manifolds with boundary},
   JOURNAL = {International Mathematics Research Notices.},
      YEAR = {2017},
    NUMBER = {12},
     PAGES = {3603--3646},
}
	
	
@article {novik_applications_2009,
    AUTHOR = {Novik, Isabella and Swartz, Ed},
     TITLE = {Applications of {K}lee's {D}ehn--{S}ommerville relations},
   JOURNAL = {Discrete \& Computational Geometry.},
    VOLUME = {42},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {261--276},
}

@article{grabe_DehnSommerville_1987,
   author={Gr\"{a}be, Hans-Gert},
   title={Generalized {D}ehn--{S}ommerville equations and an upper bound theorem},
   journal={Beitr\"{a}ge zur Algebra und Geometrie},
   number={25},
   date={1987},
   pages={47--60},
}


@article {bayer_generalized_1985,
    AUTHOR = {Bayer, Margaret M. and Billera, Louis J.},
     TITLE = {Generalized {D}ehn--{S}ommerville relations for polytopes, spheres and {E}ulerian partially ordered sets},
   JOURNAL = {Inventiones Mathematicae},
    VOLUME = {79},
      YEAR = {1985},
    NUMBER = {1},
     PAGES = {143--157},
}


@article {stanley_combinatorial_1974,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Combinatorial reciprocity theorems},
   JOURNAL = {Advances in Mathematics},
    VOLUME = {14},
      YEAR = {1974},
     PAGES = {194--253},
}

@book {bruns_cohen_1993,
    AUTHOR = {Bruns, Winfried and Herzog, J\"{u}rgen},
     TITLE = {{Cohen-{M}acaulay Rings}},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {39},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1993},
     PAGES = {xii+403},
}


@article {adiprasito_relative_2016,
    AUTHOR = {Adiprasito, Karim A. and Sanyal, Raman},
     TITLE = {Relative {S}tanley-{R}eisner theory and upper bound theorems for {M}inkowski sums},
   JOURNAL = {Publications Math\'{e}matiques. Institut de Hautes \'{E}tudes Scientifiques},
    VOLUME = {124},
      YEAR = {2016},
     PAGES = {99--163},
}


@book {stanley_combinatorics_algebra_book_1996,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {{Combinatorics and Commutative Algebra}},
    SERIES = {Progress in Mathematics},
    VOLUME = {41},
   EDITION = {2nd edition},
 PUBLISHER = {Birkh\"{a}user Boston, Inc., Boston, MA},
      YEAR = {1996},
     PAGES = {x+164},
}

@article {swartz_face_enumeration_2009,
    AUTHOR = {Swartz, Ed},
     TITLE = {Face enumeration---from spheres to manifolds},
   JOURNAL = {Journal of the European Mathematical Society},
    VOLUME = {11},
      YEAR = {2009},
    NUMBER = {3},
     PAGES = {449--485},
}

@article {klee_DehnSommervilleRelations_1964,
    AUTHOR = {Klee, Victor},
     TITLE = {A combinatorial analogue of {P}oincar\'{e}'s duality theorem},
   JOURNAL = {Canadian Journal of Mathematics. Journal Canadien de Math\'{e}matiques},
    VOLUME = {16},
      YEAR = {1964},
     PAGES = {517--531},
}

@book {CombinatorialRecirpocityBook,
    AUTHOR = {Beck, Matthias and Sanyal, Raman},
     TITLE = {{Combinatorial Reciprocity Theorems}},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {195},
      NOTE = {An invitation to enumerative geometric combinatorics},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2018},
     PAGES = {xiv+308},
}


@book {Ziegler95,
    	AUTHOR = {Ziegler, G{\"u}nter M.},
     	TITLE = {Lectures on polytopes},
    	SERIES = {Graduate Texts in Mathematics},
    	VOLUME = {152},
 	PUBLISHER = {Springer-Verlag, New York},
      	YEAR = {1995},
     	PAGES = {x+370},
}


@article {CeballosSantosZiegler2015,
    AUTHOR = {Ceballos, Cesar and Santos, Francisco and Ziegler, G{\"u}nter M.},
     TITLE = {Many non-equivalent realizations of the associahedron},
   JOURNAL = {Combinatorica},
    VOLUME = {35},
      YEAR = {2015},
    NUMBER = {5},
     PAGES = {513--551},
}

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


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

@article{FZ03,
	author = {Sergey Fomin and Andrei Zelevinsky}, 		
	title =	{{$Y$-systems and generalized associahedra}},
	JOURNAL = {Annals of Mathematics. Second Series},
	volume = 158,
	year = 2003, 
	pages = {977-1018}
}

@article{ceballos_hopf_2018,
	author = {Bergeron, Nantel and Ceballos, Cesar and Pilaud, Vincent},
	eprint = {1807.03044},
    eprinttype = {arXiv},
	title = {Hopf dreams and diagonal harmonics},
	year = {2018}
}

@article{armstrong09generalized,
	author = {Drew Armstrong},
	journal = {Memoirs of the American Mathematical Society},
	title = {Generalized noncrossing partitions and combinatorics of {C}oxeter groups},
	volume = {202},
	year = {2009}
}

 @article{ceballos19geometry,
     AUTHOR = {Ceballos, Cesar and Padrol, Arnau and Sarmiento, Camilo},
      TITLE = {Geometry of {$\nu$}-{T}amari lattices in types {$A$} and {$B$}},
    JOURNAL = {Transactions of the American Mathematical Society},
     VOLUME = {371},
       YEAR = {2019},
      PAGES = {2575--2622}
 }

@article{ceballos19sweakorder,
	author = {Cesar Ceballos and Viviane Pons},
	journal = {S{\'e}minaire Lotharingien de Combinatoire},
	note = {Proceedings of the 31st Conference on Formal Power Series and Algebraic Combinatorics},
	pages = {Conference paper 76, 12 pages},
	title = {The $s$-Weak Order and $s$-Permutahedra},
	volume = {82B},
	year = {2019}
}

@article{ceballos20nu,
	author = {Cesar Ceballos and Arnau Padrol and Camilo Sarmiento},
	journal = {The Electronic Journal of Combinatorics},
	pages = {Research paper P1.14, 31 pages},
	title = {The $\nu$-{T}amari lattice via $\nu$-trees, $\nu$-bracket vectors, and subword complexes},
	volume = {27},
	year = {2020}
}

@article{ceballos20the,
	author = {Cesar Ceballos and Wenjie Fang and Henri M{\"u}hle},
	journal = {Journal of Combinatorial Theory (Series A)},
	pages = {Article 105210, 59 pages},
	title = {The {S}teep-{B}ounce zeta map in {P}arabolic {C}ataland},
	volume = {172},
	year = {2020}
}

@article{chapoton06sur,
	author = {Fr{\'e}d{\'e}ric Chapoton},
	journal = {Bulletin of the Belgian Mathematical Society},
	pages = {585--596},
	title = {Sur le nombre de r{\'e}flexions pleines dans les groupes de {C}oxeter finis},
	volume = {13},
	year = {2006}
}

@article{garver17enumerative,
	author = {Alexander Garver and Thomas McConville},
	eprint = {1705.04901},
    eprinttype = {arXiv},
	title = {Enumerative properties of grid-associahedra},
	year = {2017}
}

@article{krattenthaler19the,
	author = {Christian Krattenthaler and Henri M{\"u}hle},
	eprint = {1910.13244},
    eprinttype = {arXiv},
	title = {The rank enumeration of certain parabolic non-crossing partitions},
	year = {2019}
}

@article{muehle21noncrossing,
	author = {Henri M{\"u}hle},
	journal = {Annals of Combinatorics},
	title = {Noncrossing arc diagrams, {T}amari lattices, and parabolic quotients of the symmetric group},
	year = {2021},
	note = {To appear.}
}

@article{muehle19ballot,
	author = {Henri M{\"u}hle},
	journal = {S{\'e}minaire Lotharingien de Combinatoire},
	note = {Proceedings of the 31st Conference on Formal Power Series and Algebraic Combinatorics},
	pages = {Conference paper 7, 12 pages},
	title = {Ballot-noncrossing partitions},
	volume = {82B},
	year = {2019}
}

@article{muehle20hochschild,
	author = {Henri M{\"u}hle},
	eprint = {2008.13247},
    eprinttype = {arXiv},
	title = {Hochschild lattices and shuffle lattices},
	year = {2020}
}

@article{preville17enumeration,
	author = {Louis-Fran{\c c}ois Pr{\'e}ville-Ratelle and Xavier Viennot},
	journal = {Transactions of the American Mathematical Society},
	pages = {5219--5239},
	title = {The enumeration of generalized {T}amari intervals},
	volume = {369},
	year = {2017}
}

@article{thiel14on,
	author = {Marko Thiel},
	journal = {European Journal of Combinatorics},
	pages = {244--255},
	title = {On the {$H$}-triangle of generalised nonnesting partitions},
	volume = {39},
	year = {2014}
}

@article{barnard19canonical,
	author = {Emily Barnard},
	journal = {The Electronic Journal of Combinatorics},
	pages = {Research paper P1.24, 25 pages},
	title = {The canonical join complex},
	volume = {26},
	year = {2019}
}

@article{muehle19the,
	author = {Henri M{\"u}hle},
	journal = {Algebra Universalis},
	pages = {Research paper 10, 22 pages},
	title = {The core label order of a congruence-uniform lattice},
	volume = {80},
	year = {2019}
}

@article{reading11noncrossing,
	author = {Nathan Reading},
	journal = {Journal of Algebraic Combinatorics},
	pages = {483--530},
	title = {Noncrossing partitions and the shard intersection order},
	volume = {33},
	year = {2011}
}

@misc{sloane,
	author = {Neil J. A. Sloane},
	title = {The on-line encyclopedia of integer sequences},
	note = {\url{https://oeis.org}}
}