Semirings in which the permanent of invertible matrices is multiplicative

We show that, if $1+2xy=1$ holds for all elements $x,\,y$ with additive inverses in a commutative semiring $\mathcal{S}$, then the function of permanent is multiplicative on the matrices with multiplicative inverses over $\mathcal{S}$.

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Publication Details

Journal
Electronic Journal of Linear Algebra
Published
2025-02-23
DOI
https://doi.org/10.13001/ela.2025.9163
Primary Topic
Advanced Topics in Algebra
Type
article
Field-Weighted Citation Impact
0.00
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article

Semirings in which the permanent of invertible matrices is multiplicative

Yaroslav Shitov
Electronic Journal of Linear Algebra
Advanced Topics in Algebra
article

Semirings in which the permanent of invertible matrices is multiplicative

Yaroslav Shitov
article en

Abstract

We show that, if $1+2xy=1$ holds for all elements $x,\,y$ with additive inverses in a commutative semiring $\mathcal{S}$, then the function of permanent is multiplicative on the matrices with multiplicative inverses over $\mathcal{S}$.

Electronic Journal of Linear AlgebraVol. 41
Openalex Percentile: Top 94%
Advanced Topics in Algebra
DOIOpen Access PDFOpenAlex
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Semirings in which the permanent of invertible matrices is multiplicative — Yaroslav Shitov · Electronic Journal of Linear Algebra (2025) | TGRS Research Map | TGRS