@book {GratzerWehrung-LatticeTheoryI,
	TITLE = {Lattice theory: special topics and applications. {V}ol. 2},
	EDITOR = {Gr\"{a}tzer, George and Wehrung, Friedrich},
	PUBLISHER = {Birkh\"{a}user/Springer, Cham},
	YEAR = {2016},
	PAGES = {xv+616},
}
		
@book {GratzerWehrung-LatticeTheoryII,
	TITLE = {Lattice theory: special topics and applications. {V}ol. 1},
	EDITOR = {Gr\"{a}tzer, George and Wehrung, Friedrich},
	PUBLISHER = {Birkh\"{a}user/Springer, Cham},
	YEAR = {2014},
	PAGES = {xiv+468},
}

@article {Day,
	AUTHOR = {Day, Alan},
	TITLE = {Congruence normality: the characterization of the doubling class of convex sets},
	JOURNAL = {Algebra Universalis},
	FJOURNAL = {Algebra Universalis},
	VOLUME = {31},
	YEAR = {1994},
	NUMBER = {3},
	PAGES = {397--406},
}

@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-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 James B. Nation},
	TITLE = {Free lattices},
	JOURNAL = {Mathematical Surveys and Monographs},
	YEAR = {1995},
	VOLUME = {75},
	PAGES = {93--106}
}

@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}
}

@article {Barnard,
	AUTHOR = {Barnard, Emily},
	TITLE = {The canonical join complex},
	JOURNAL = {Electron. J. Combin.},
	FJOURNAL = {Electronic Journal of Combinatorics},
	VOLUME = {26},
	YEAR = {2019},
	NUMBER = {1},
	PAGES = {\# 1.24, 25},
}

@article {BarnardMcConville,
	AUTHOR = {Barnard, Emily and McConville, Thomas},
	TITLE = {Lattices from graph associahedra and subalgebras of the {M}alvenuto-{R}eutenauer algebra},
	JOURNAL = {Algebra Universalis},
	FJOURNAL = {Algebra Universalis},
	VOLUME = {82},
	YEAR = {2021},
	NUMBER = {1},
	PAGES = {Paper No. 2, 53},
}

@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 {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 {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},
}

@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. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A},
	VOLUME = {13},
	YEAR = {1972},
	PAGES = {\mbox{7--13}},
}

@misc {AlbertinPilaud,
	AUTHOR = {Doriann Albertin and Vincent Pilaud},
	TITLE = {The canonical complex of the weak order},
    EPRINT = {2111.11553},
    EPRINTTYPE = {arxiv},
	YEAR = {2021},
}

% sage, OEIS

@manual {Sage,
	AUTHOR = {The {S}age developers},
	TITLE = {{S}age {M}athematics {S}oftware},
	NOTE = {\url{http://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 = {\url{http://oeis.org}},
	YEAR = {2010},
}