The Marcus–Minc Transform Inequality

We prove the Marcus–Minc conjecture: if n ≥ 2 is an integer, A is a nonnegative n × n matrix whose row and column sums equal one, and Jn has every entry 1/n, then per A ≥ per((nJn − A)/(n − 1)). We also determine all equality cases. 2020 Mathematics Subject Classification: 15A15, 05A20, 15B51.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-24
DOI
https://doi.org/10.5281/zenodo.22927879
Primary Topic
Polynomial and algebraic computation
Type
preprint
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preprint

The Marcus–Minc Transform Inequality

Yair Lavi
Zenodo (CERN European Organization for Nuclear Research)
Polynomial and algebraic computation
preprint

The Marcus–Minc Transform Inequality

Yair Lavi
preprint en

Abstract

We prove the Marcus–Minc conjecture: if n ≥ 2 is an integer, A is a nonnegative n × n matrix whose row and column sums equal one, and Jn has every entry 1/n, then per A ≥ per((nJn − A)/(n − 1)). We also determine all equality cases. 2020 Mathematics Subject Classification: 15A15, 05A20, 15B51.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Polynomial and algebraic computation
DOIOpen Access PDFOpenAlex
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The Marcus–Minc Transform Inequality — Yair Lavi · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS