GROUPS OF SINGULAR ALTERNATING SIGN MATRICES*

Cian O’brien; Rachel Quinlan

doi:10.13001/ela.2025.8715

GROUPS OF SINGULAR ALTERNATING SIGN MATRICES^*

Cian O’brien
, Rachel Quinlan

Mary Immaculate College
School of Mathematical and Statistical Science
University of Galway

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

Abstract

We investigate multiplicative groups consisting entirely of singular alternating sign matrices (ASMs) and present several constructions of such groups. It is shown that every finite group is isomorphic to a group of singular ASMs, with a singular idempotent ASM as its identity element. The relationship between the size, the rank, and the possible multiplicative orders of singular ASMs is explored.

Original language	English
Pages (from-to)	288-303
Number of pages	16
Journal	Electronic Journal of Linear Algebra
Volume	41
DOIs	https://doi.org/10.13001/ela.2025.8715
Publication status	Published - 1 Jan 2025
Externally published	Yes

Keywords

Alternating sign matrix
Matrix group

Access to Document

10.13001/ela.2025.8715

Cite this

@article{463a9ac704f145aa957be8ca7f88266d,

title = "GROUPS OF SINGULAR ALTERNATING SIGN MATRICES*",

abstract = "We investigate multiplicative groups consisting entirely of singular alternating sign matrices (ASMs) and present several constructions of such groups. It is shown that every finite group is isomorphic to a group of singular ASMs, with a singular idempotent ASM as its identity element. The relationship between the size, the rank, and the possible multiplicative orders of singular ASMs is explored.",

keywords = "Alternating sign matrix, Matrix group",

author = "Cian O{\textquoteright}brien and Rachel Quinlan",

year = "2025",

month = jan,

day = "1",

doi = "10.13001/ela.2025.8715",

language = "English",

volume = "41",

pages = "288--303",

journal = "Electronic Journal of Linear Algebra",

issn = "1537-9582",

publisher = "International Linear Algebra Society",

}

TY - JOUR

T1 - GROUPS OF SINGULAR ALTERNATING SIGN MATRICES*

AU - O’brien, Cian

AU - Quinlan, Rachel

PY - 2025/1/1

Y1 - 2025/1/1

N2 - We investigate multiplicative groups consisting entirely of singular alternating sign matrices (ASMs) and present several constructions of such groups. It is shown that every finite group is isomorphic to a group of singular ASMs, with a singular idempotent ASM as its identity element. The relationship between the size, the rank, and the possible multiplicative orders of singular ASMs is explored.

AB - We investigate multiplicative groups consisting entirely of singular alternating sign matrices (ASMs) and present several constructions of such groups. It is shown that every finite group is isomorphic to a group of singular ASMs, with a singular idempotent ASM as its identity element. The relationship between the size, the rank, and the possible multiplicative orders of singular ASMs is explored.

KW - Alternating sign matrix

KW - Matrix group

UR - https://www.scopus.com/pages/publications/105006902728

U2 - 10.13001/ela.2025.8715

DO - 10.13001/ela.2025.8715

M3 - Article

AN - SCOPUS:105006902728

SN - 1537-9582

VL - 41

SP - 288

EP - 303

JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

ER -

GROUPS OF SINGULAR ALTERNATING SIGN MATRICES^*

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this