PreprintCC BY 4.0arXiv
The Marcus-Minc Transform Inequality
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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BibTeX
@misc{lavi2026marcusminc,
title = {{The Marcus-Minc Transform Inequality}},
author = {Yair Lavi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29262},
eprint = {2609.29262},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29262},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Marcus-Minc Transform Inequality
AU - Yair Lavi
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29262
UR - https://arxiv.org/abs/2609.29262
AB - 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.
ER -