Abstract
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 language | English |
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Pages (from-to) | 1171-1197 |
Number of pages | 27 |
Journal | Journal of Algebraic Combinatorics |
Volume | 55 |
Issue number | 4 |
DOIs | |
State | Published - Jun 2022 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Breakpoint graph
- Commuting probability
- Finite group
- Signed Hultman number
- Signed permutation