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@article{Reading-posetRegions,
	Author = {Reading, Nathan},
	Date-Added = {2019-04-24 13:22:45 +1000},
	Date-Modified = {2019-04-24 13:23:14 +1000},
	Doi = {10.1007/s00012-003-1834-0},
	Fjournal = {Algebra Universalis},
	Journal = {Algebra Universalis},
	Number = {2},
	Pages = {179--205},
	Title = {Lattice and order properties of the poset of regions in a hyperplane arrangement},
	Volume = {50},
	Year = {2003}}

@article{Pilaud-arcDiagramAlgebra,
	Author = {Pilaud, Vincent},
	Date-Added = {2019-04-24 13:21:36 +1000},
	Date-Modified = {2019-04-24 13:22:02 +1000},
	Doi = {10.1016/j.jcta.2018.09.005},
	Fjournal = {Journal of Combinatorial Theory. Series A},
	Journal = {J. Combin. Theory Ser. A},
	Pages = {486--507},
	Title = {Hopf algebras on decorated noncrossing arc diagrams},
	Volume = {161},
	Year = {2019}}

@article{NovelliThibon-coloredHopfAlgebras,
	Author = {Novelli, Jean-Christophe and Thibon, Jean-Yves},
	Date-Added = {2019-04-24 13:20:42 +1000},
	Date-Modified = {2019-04-24 13:21:15 +1000},
	Doi = {10.1016/j.disc.2010.09.008},
	Fjournal = {Discrete Mathematics},
	Journal = {Discrete Math.},
	Number = {24},
	Pages = {3584--3606},
	Title = {Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions},
	Volume = {310},
	Year = {2010}}

@article{LodayRonco,
	Author = {Loday, Jean-Louis and Ronco, Mar{\'{\i}}a O.},
	Date-Added = {2019-04-24 13:19:18 +1000},
	Date-Modified = {2019-04-24 13:20:16 +1000},
	Doi = {10.1006/aima.1998.1759},
	Fjournal = {Advances in Mathematics},
	Journal = {Adv. Math.},
	Number = {2},
	Pages = {293--309},
	Title = {Hopf algebra of the planar binary trees},
	Volume = {139},
	Year = {1998}}

@article{PilaudSantos-brickPolytope,
	Author = {Vincent Pilaud and Francisco Santos},
	Date-Added = {2019-04-24 13:18:15 +1000},
	Date-Modified = {2019-04-24 13:18:46 +1000},
	Doi = {10.1016/j.ejc.2011.12.003},
	Fjournal = {European Journal of Combinatorics},
	Journal = {European J. Combin.},
	Number = {4},
	Pages = {632--662},
	Title = {The brick polytope of a sorting network},
	Volume = {33},
	Year = {2012}}

@article{HohlwegLange,
	Author = {Christophe Hohlweg and Carsten Lange},
	Date-Added = {2019-04-24 13:17:10 +1000},
	Date-Modified = {2019-04-24 13:17:56 +1000},
	Doi = {10.1007/s00454-007-1319-6},
	Fjournal = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	Journal = {Discrete Comput. Geom.},
	Number = {4},
	Pages = {517--543},
	Title = {Realizations of the associahedron and cyclohedron},
	Volume = {37},
	Year = {2007}}

@article{Loday,
	Author = {Jean-Louis Loday},
	Date-Added = {2019-04-24 13:16:09 +1000},
	Date-Modified = {2019-04-24 13:16:53 +1000},
	Doi = {10.1007/s00013-004-1026-y},
	Fjournal = {Archiv der Mathematik},
	Journal = {Arch. Math.},
	Number = {3},
	Pages = {267--278},
	Title = {Realization of the {S}tasheff polytope},
	Volume = {83},
	Year = {2004}}

@article{Reading-HopfAlgebras,
	Author = {Reading, N.},
	Date-Added = {2019-04-24 10:57:16 +1000},
	Date-Modified = {2019-04-24 10:57:48 +1000},
	Doi = {10.1016/j.jcta.2004.11.001},
	Fjournal = {Journal of Combinatorial Theory. Series A},
	Journal = {J. Combin. Theory Ser. A},
	Number = {2},
	Pages = {237--273},
	Title = {Lattice congruences, fans and {H}opf algebras},
	Volume = {110},
	Year = {2005},
	Bdsk-Url-1 = {https://doi.org/10.1016/j.jcta.2004.11.001}}

@incollection{Reading-surveyChapters,
	Author = {Reading, Nathan},
	Booktitle = {Lattice Theory: Special Topics and Applications. {V}ol. 2},
	Date-Added = {2019-04-24 10:56:40 +1000},
	Date-Modified = {2019-04-24 13:14:11 +1000},
	Pages = {399--561},
	Publisher = {Birkh\"auser/Springer},
	Title = {Lattice theory of the poset of regions \& Finite {C}oxeter groups and the weak order},
	Year = {2016}}

@article{Reading-arcDiagrams,
	Author = {Reading, N.},
	Date-Added = {2019-04-24 10:55:32 +1000},
	Date-Modified = {2019-04-24 10:55:57 +1000},
	Doi = {10.1137/140972391},
	Fjournal = {SIAM Journal on Discrete Mathematics},
	Journal = {SIAM J. Discrete Math.},
	Number = {2},
	Pages = {736--750},
	Title = {Noncrossing arc diagrams and canonical join representations},
	Volume = {29},
	Year = {2015},
	Bdsk-Url-1 = {https://doi.org/10.1137/140972391}}

@article{LawReading,
	Author = {Law, S. and Reading, N.},
	Date-Added = {2019-04-24 10:54:44 +1000},
	Date-Modified = {2019-04-24 10:55:13 +1000},
	Doi = {10.1016/j.jcta.2011.09.006},
	Fjournal = {Journal of Combinatorial Theory. Series A},
	Journal = {J. Combin. Theory Ser. A},
	Number = {3},
	Pages = {788--824},
	Title = {The {H}opf algebra of diagonal rectangulations},
	Volume = {119},
	Year = {2012},
	Bdsk-Url-1 = {https://doi.org/10.1016/j.jcta.2011.09.006}}

@article{Pilaud-brickAlgebra,
	Author = {V. Pilaud},
	Date-Added = {2019-04-24 10:53:55 +1000},
	Date-Modified = {2019-04-24 10:54:28 +1000},
	Doi = {10.1016/j.jcta.2017.11.014},
	Fjournal = {Journal of Combinatorial Theory. Series A},
	Journal = {J. Combin. Theory Ser. A},
	Pages = {418--457},
	Title = {Brick polytopes, lattice quotients, and {H}opf algebras},
	Volume = {155},
	Year = {2018},
	Bdsk-Url-1 = {https://doi.org/10.1016/j.jcta.2017.11.014}}

@article{PilaudPons-permutrees,
	Author = {Pilaud, V. and Pons, V.},
	Date-Added = {2019-04-24 10:52:50 +1000},
	Date-Modified = {2019-04-24 10:53:22 +1000},
	Doi = {10.5802/alco.1},
	Fjournal = {Algebraic Combinatorics},
	Journal = {Algebr. Combin.},
	Number = {2},
	Pages = {173-224},
	Publisher = {MathOA foundation},
	Title = {Permutrees},
	Volume = {1},
	Year = {2018},
	Bdsk-Url-1 = {https://doi.org/10.5802/alco.1}}

@article{ChatelPilaud,
	Author = {G. Chatel and V. Pilaud},
	Date-Added = {2019-04-24 10:51:59 +1000},
	Date-Modified = {2019-04-24 10:52:30 +1000},
	Doi = {10.1016/j.aim.2017.02.027},
	Fjournal = {Advances in Mathematics},
	Journal = {Adv. Math.},
	Pages = {598--633},
	Title = {{C}ambrian {H}opf {Algebras}},
	Volume = {311},
	Year = {2017},
	Bdsk-Url-1 = {https://doi.org/10.1016/j.aim.2017.02.027}}

@article{Reading-CambrianLattices,
	Author = {N. Reading},
	Date-Added = {2019-04-24 10:50:39 +1000},
	Date-Modified = {2019-04-24 10:51:28 +1000},
	Doi = {10.1016/j.aim.2005.07.010},
	Fjournal = {Advances in Mathematics},
	Journal = {Adv. Math.},
	Number = {2},
	Pages = {313--353},
	Title = {Cambrian lattices},
	Volume = {205},
	Year = {2006},
	Bdsk-Url-1 = {https://doi.org/10.1016/j.aim.2005.07.010}}

@article{HivertNovelliThibon-algebraBinarySearchTrees,
	Author = {Hivert, F. and Novelli, J.-C. and Thibon, J.-Y.},
	Date-Added = {2019-04-24 10:49:22 +1000},
	Date-Modified = {2019-04-24 10:50:13 +1000},
	Doi = {10.1016/j.tcs.2005.01.012},
	Fjournal = {Theoretical Computer Science},
	Journal = {Theoret. Comput. Sci.},
	Number = {1},
	Pages = {129--165},
	Title = {The algebra of binary search trees},
	Volume = {339},
	Year = {2005},
	Bdsk-Url-1 = {https://doi.org/10.1016/j.tcs.2005.01.012}}

@article{MalvenutoReutenauer,
	Author = {Malvenuto, C. and Reutenauer, C.},
	Date-Added = {2019-04-24 10:47:55 +1000},
	Date-Modified = {2019-04-24 10:48:59 +1000},
	Doi = {10.1006/jabr.1995.1336},
	Fjournal = {Journal of Algebra},
	Journal = {J. Algebra},
	Number = {3},
	Pages = {967--982},
	Title = {Duality between quasi-symmetric functions and the {S}olomon descent algebra},
	Volume = {177},
	Year = {1995},
	Bdsk-Url-1 = {https://doi.org/10.1006/jabr.1995.1336}}

@misc{PilaudSantos-quotientopes,
	Author = {V. Pilaud and F. Santos},
	Date-Added = {2019-04-24 10:45:18 +1000},
	Date-Modified = {2019-04-24 10:47:17 +1000},
	Eprint = {1711.05353},
	Eprinttype = {arXiv},
	Title = {Quotientopes},
	Year = {2017}}