The Kopotun Subpermanent Transform Inequality
2026-10-11
Research publication
The Kopotun Subpermanent Transform Inequality
Preprint
- Original date
- Authors
- Yair Lavi
- Combinatorics
- Matrix theory
- Permanents
- Doubly stochastic matrices
Abstract
We prove the subpermanent transform inequality conjectured by Kopotun in 1996: for every doubly stochastic matrix \(A\) of order \(n\ge2\) and every \(2\le k\le n\),
\[ \sigma_k(A)\ge\sigma_k\!\left(\frac{nJ_n+A}{n+1}\right). \]
Here \(\sigma_k\) is the sum of all subpermanents of order \(k\), and \(J_n\) has every entry \(1/n\). Equality holds exactly at \(A=J_n\).