Separable elements in Weyl groups

DOI10.1016/j.aam.2019.101974zbMath1429.05003arXiv1905.09331OpenAlexW3105827076WikidataQ126758304 ScholiaQ126758304MaRDI QIDQ2280364

Yibo Gao, Christian Gaetz

Publication date: 18 December 2019

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.09331

zbMATH Keywords

generating functionsymmetric groupseparable permutationsproduct decompositionsweak Bruhat order

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Permutations, words, matrices (05A05) Grassmannians, Schubert varieties, flag manifolds (14M15) Simple, semisimple, reductive (super)algebras (17B20) Algebraic aspects of posets (06A11) Root systems (17B22) Combinatorial aspects of groups and algebras (05E16)

Related Items

The hull metric on Coxeter groups, Diameters of graphs of reduced words and rank-two root subsystems, Consecutive patterns in Coxeter groups, Separable elements: linear extensions, graph associahedra, and splittings of Weyl groups, Separable elements and splittings of Weyl groups, Counting shellings of complete bipartite graphs and trees

Cites Work

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• Pattern matching for permutations
• Product decompositions of the symmetric group induced by separable permutations
• Generating trees and the Catalan and Schröder numbers
• The weak Bruhat order on the symmetric group is Sperner
• Smoothness of Schubert varieties via patterns in root subsystems
• Combinatorics of Coxeter Groups
• Generalized Quotients in Coxeter Groups
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property
• Bootstrap Percolation, the Schröder Numbers, and theN-Kings Problem