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The Marcus-Minc Transform Inequality

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Contributed by Yair Lavi ↗

Version 1 / Nov 12, 2026/ arXiv: 2609.29262 / CC BY 4.0

Abstract

We prove the Marcus-Minc conjecture: let n be any integer at least 2, and let A be a nonnegative n by n matrix whose row and column sums are all one. Form a new matrix by subtracting A from the n by n matrix of ones and dividing by n minus one. Then the permanent of A is at least the permanent of the new matrix. We also determine all equality cases.

Tools used

OpenAI
GPT-5.6-sol
OpenAI
GPT-6 Astra
Anthropic
Claude FableVersion 5

References

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  1. M. Laurent and A. Schrijver, ``On Leonid Gurvits's Proof for Permanents,'' American Mathematical Monthly 117 (2010), 903--911. doi:10.4169/000298910X523380 (https://doi.org/10.4169/000298910X523380).DOI

Version history

  1. v1 · 11 pagesSubmitted by Yair LaviInitial depositCurrentNov 11, 2026