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arXiv · 2609.29262

The Marcus-Minc Transform Inequality

Yair Lavi
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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.

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Yair Lavi. 2026-09-24. The Marcus-Minc Transform Inequality. https://arxiv.org/abs/2609.29262

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