Signed Hultman numbers and signed generalized commuting probability in finite groups

Robert Shwartz, Vadim E. Levit

Research output: Contribution to journalArticlepeer-review


Let G be a finite group. Let π be a permutation from Sn. We study the distribution of probabilities of equalitya1a2⋯an-1an=aπ1ϵ1aπ2ϵ2⋯aπn-1ϵn-1aπnϵn, when π varies over all the permutations in Sn, and ϵi varies over the set { + 1 , - 1 }. By [7], the case where all ϵi are + 1 led to a close connection to Hultman numbers. In this paper, we generalize the results, permitting ϵi to be - 1. We describe the spectrum of the probabilities of signed permutation equalities in a finite group G. This spectrum turns out to be closely related to the partition of 2 n· n! into a sum of the corresponding signed Hultman numbers.

Original languageEnglish
Pages (from-to)1171-1197
Number of pages27
JournalJournal of Algebraic Combinatorics
Issue number4
StatePublished - Jun 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Breakpoint graph
  • Commuting probability
  • Finite group
  • Signed Hultman number
  • Signed permutation


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