The Marcus–Minc Transform Inequality
2026-09-24
Research publication
The Marcus–Minc Transform Inequality
arXiv preprint
- Original date
- Authors
- Yair Lavi
- Combinatorics
- Matrix theory
- Permanents
- Doubly stochastic matrices
Abstract
We prove the Marcus–Minc conjecture: if \(n\ge2\) is an integer, \(A\) is a nonnegative \(n\times n\) matrix whose row and column sums equal one, and \(J_n\) has every entry \(1/n\), then
\[ \operatorname{per}A\ge\operatorname{per}\left(\frac{nJ_n-A}{n-1}\right). \]
We also determine all equality cases.