Polytopal realizations and Hopf algebra structures for lattice quotients of the weak order

zbMath1436.05006MaRDI QIDQ2306484

Vincent Pilaud

Publication date: 23 March 2020

Published in: Séminaire Lotharingien de Combinatoire (Search for Journal in Brave)

Full work available at URL: http://www.mat.univie.ac.at/~slc/wpapers/FPSAC2019//3.html

zbMATH Keywords

Hopf algebrasweak orderlattice quotientarc diagramsquotientopes

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Permutations, words, matrices (05A05) Hopf algebras and their applications (16T05)

Cites Work

• The brick polytope of a sorting network
• Lattice congruences, fans and Hopf algebras.
• The algebra of binary search trees
• Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions
• The Hopf algebra of diagonal rectangulations.
• Hopf algebra of the planar binary trees
• Hopf algebras on decorated noncrossing arc diagrams
• Brick polytopes, lattice quotients, and Hopf algebras
• Realization of the Stasheff polytope
• Duality between quasi-symmetric functions and the Solomon descent algebra
• Realizations of the associahedron and cyclohedron
• Cambrian Hopf algebras
• Lattice and order properties of the poset of regions in a hyperplane arrangement
• Cambrian lattices.
• Noncrossing Arc Diagrams and Canonical Join Representations
• Permutrees

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