Signed Hultman numbers and signed generalized commuting probability in finite groups

Robert Shwartz; Vadim E. Levit

doi:10.1007/s10801-021-01089-9

Signed Hultman numbers and signed generalized commuting probability in finite groups

Robert Shwartz, Vadim E. Levit

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

Abstract

Let G be a finite group. Let π be a permutation from S_n. We study the distribution of probabilities of equalitya1a2⋯an-1an=aπ1ϵ1aπ2ϵ2⋯aπn-1ϵn-1aπnϵn, when π varies over all the permutations in S_n, and ϵ_i varies over the set { + 1 , - 1 }. By [7], the case where all ϵ_i are + 1 led to a close connection to Hultman numbers. In this paper, we generalize the results, permitting ϵ_i 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
Pages (from-to)	1171-1197
Number of pages	27
Journal	Journal of Algebraic Combinatorics
Volume	55
Issue number	4
DOIs	https://doi.org/10.1007/s10801-021-01089-9
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

Access to Document

10.1007/s10801-021-01089-9

Cite this

@article{93fc7c0a5b3441c7bd9d6e44d2fdb00e,

title = "Signed Hultman numbers and signed generalized commuting probability in finite groups",

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.",

keywords = "Breakpoint graph, Commuting probability, Finite group, Signed Hultman number, Signed permutation",

author = "Robert Shwartz and Levit, {Vadim E.}",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2022",

month = jun,

doi = "10.1007/s10801-021-01089-9",

language = "אנגלית",

volume = "55",

pages = "1171--1197",

journal = "Journal of Algebraic Combinatorics",

issn = "0925-9899",

publisher = "Springer Netherlands",

number = "4",

}

TY - JOUR

T1 - Signed Hultman numbers and signed generalized commuting probability in finite groups

AU - Shwartz, Robert

AU - Levit, Vadim E.

PY - 2022/6

Y1 - 2022/6

N2 - 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.

AB - 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.

KW - Breakpoint graph

KW - Commuting probability

KW - Finite group

KW - Signed Hultman number

KW - Signed permutation

UR - http://www.scopus.com/inward/record.url?scp=85122157426&partnerID=8YFLogxK

U2 - 10.1007/s10801-021-01089-9

DO - 10.1007/s10801-021-01089-9

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85122157426

SN - 0925-9899

VL - 55

SP - 1171

EP - 1197

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

IS - 4

ER -

Signed Hultman numbers and signed generalized commuting probability in finite groups

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this