Algebraic structures on integer posets

zbMath1411.05295MaRDI QIDQ2632699

Vincent Pilaud, Viviane Pons

Publication date: 15 May 2019

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

Full work available at URL: http://www.mat.univie.ac.at/~slc/wpapers/FPSAC2018//61-Pilaud-Pons.html

zbMATH Keywords

polytopesHopf algebra

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Combinatorics of partially ordered sets (06A07) Hopf algebras and their applications (16T05)

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Cites Work

• The algebra of binary search trees
• The Hopf algebra of integer binary relations
• Permutation statistics and linear extensions of posets
• Hopf algebra of the planar binary trees
• The weak order on integer posets
• Noncommutative symmetric functions
• Realization of the Stasheff polytope
• Duality between quasi-symmetric functions and the Solomon descent algebra
• Hopf algebras of permutahedra, associahedra and hypercubes
• Cambrian Hopf algebras
• Weak Bruhat order on the set of faces of the permutohedron and the associahedron.
• Cambrian lattices.
• Lattice congruences of the weak order.
• The facial weak order and its lattice quotients
• Permutrees