The Wang Transform Inequality
2026-09-24
Research publication
The Wang Transform Inequality
Preprint
- Original date
- Authors
- Yair Lavi
- Combinatorics
- Matrix theory
- Permanents
- Doubly stochastic matrices
Abstract
We prove the Wang transform inequality in every order: if \(n\) is a positive 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
\[ \operatorname{per}A\ge\operatorname{per}\!\left(\frac{nJ_n+A}{n+1}\right). \]
Equality holds exactly when \(A=J_n\). We also obtain an explicit positive quadratic gap for every \(n\ge2\).