Matrices, characters and descents

Ron M. Adin; Yuval Roichman

doi:https://doi.org/10.1016/j.laa.2014.11.028

Matrices, characters and descents

Ron M. Adin, Yuval Roichman

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

A new family of asymmetric matrices of Walsh-Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss their eigenvalues. The invertibility of these matrices implies that certain character formulas are invertible, yielding expressions for the cardinalities of sets of combinatorial objects with prescribed descent sets in terms of character values of the symmetric group.

Original language	English
Pages (from-to)	381-418
Number of pages	38
Journal	Linear Algebra and Its Applications
Volume	469
DOIs	https://doi.org/10.1016/j.laa.2014.11.028
State	Published - 15 Mar 2015

Keywords

Character formulas
Descents
Symmetric group
WalshHadamard matrices

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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https://doi.org/10.1016/j.laa.2014.11.028

Cite this

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title = "Matrices, characters and descents",

abstract = "A new family of asymmetric matrices of Walsh-Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss their eigenvalues. The invertibility of these matrices implies that certain character formulas are invertible, yielding expressions for the cardinalities of sets of combinatorial objects with prescribed descent sets in terms of character values of the symmetric group.",

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AU - Adin, Ron M.

AU - Roichman, Yuval

PY - 2015/3/15

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N2 - A new family of asymmetric matrices of Walsh-Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss their eigenvalues. The invertibility of these matrices implies that certain character formulas are invertible, yielding expressions for the cardinalities of sets of combinatorial objects with prescribed descent sets in terms of character values of the symmetric group.

AB - A new family of asymmetric matrices of Walsh-Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss their eigenvalues. The invertibility of these matrices implies that certain character formulas are invertible, yielding expressions for the cardinalities of sets of combinatorial objects with prescribed descent sets in terms of character values of the symmetric group.

KW - Character formulas

KW - Descents

KW - Symmetric group

KW - WalshHadamard matrices

UR - http://www.scopus.com/inward/record.url?scp=84917706838&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.laa.2014.11.028

DO - https://doi.org/10.1016/j.laa.2014.11.028

M3 - مقالة

SN - 0024-3795

VL - 469

SP - 381

EP - 418

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Matrices, characters and descents

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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