Matrices, characters and descents

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21 Scopus citations


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 languageEnglish
Pages (from-to)381-418
Number of pages38
JournalLinear Algebra and Its Applications
StatePublished - 15 Mar 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc. All rights reserved.


  • Character formulas
  • Descents
  • Symmetric group
  • WalshHadamard matrices


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