Character formulas and descents for the hyperoctahedral group

DOI10.1016/j.aam.2017.01.004zbMath1364.05087arXiv1504.01283OpenAlexW2962927846MaRDI QIDQ2356773

Christos A. Athanasiadis, Yuval Roichman, Sergi Elizalde, Ron M. Adin

Publication date: 6 June 2017

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

Full work available at URL: https://arxiv.org/abs/1504.01283

zbMATH Keywords

charactersymmetric grouphyperoctahedral groupderangementquasisymmetric functiondescent setSchur-positivity

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Boolean and Hadamard matrices (15B34)

Related Items

Hultman elements for the hyperoctahedral groups, On rotated Schur-positive sets, Block decomposition of permutations and Schur-positivity, The symmetric group action on rank-selected posets of injective words, A link between the generating function of skew domino tableaux and quasisymmetric functions of type B, Specializations of colored quasisymmetric functions, The Eulerian distribution on the fixed-point free involutions of the hyperoctahedral group, Schur-positive sets of permutations via products and grid classes, Gamma-positivity in combinatorics and geometry, A new link between the descent algebra of type B, domino tableaux and Chow's quasisymmetric functions, Specializations of colored quasisymmetric functions and Euler-Mahonian identities, \(k\)-partial permutations and the center of the wreath product \(\mathcal{S}_k\wr\mathcal{S}_n\) algebra, Unnamed Item, Some applications of Rees products of posets to equivariant gamma-positivity, A \(q\)-deformed type B Cauchy identity and Chow's quasisymmetric functions, Block number, descents and Schur positivity of fully commutative elements in \(B_n\), The Eulerian distribution on the involutions of the hyperoctahedral group is unimodal

Cites Work

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• Triangle-free triangulations, hyperplane arrangements and shifted tableaux
• Matrices, characters and descents
• Colored posets and colored quasisymmetric functions
• Knuth relations for the hyperoctahedral groups
• Combinatorial Gelfand models.
• Complexes of injective words and their commutation classes
• A Schensted algorithm for rim hook tableaux
• On the eigenvalues of representations of reflection groups and wreath products
• Some aspects of groups acting on finite posets
• The root number function in symmetric groups
• Counting permutations with given cycle structure and descent set
• Descent classes of permutations with a given number of fixed points
• A recursive rule for Kazhdan-Lusztig characters
• Cycle type and descent set in wreath products
• Projective reflection groups.
• On characters of Weyl groups
• The combinatorics of the bar resolution in group cohomology
• Schubert polynomials, Kazhdan-Lusztig basis and characters
• Arc permutations
• On Kazhdan-Lusztig cells in type \(B\).
• Power sum expansion of chromatic quasisymmetric functions
• A note on the number of \(k\)-roots in \(S_{n}\)
• Signed arc permutations
• Flag weak order on wreath products
• Eigenvalues of the Adin-Roichman matrices
• Coloured peak algebras and Hopf algebras.
• A note on three types of quasisymmetric functions
• Descents of derangements and circular words
• Combinatorics of Coxeter Groups
• Signed words and permutations, I: A fundamental transformation
• Invariants of finite groups and their applications to combinatorics
• Major Index and Inversion Number of Permutations
• On the Netto Inversion Number of a Sequence
• The flag major index and group actions on polynomial rings.