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The Wang Transform Inequality

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Contributed by Yair Lavi ↗

Version 1 / Nov 11, 2026/ arXiv: 2609.31794 / CC BY 4.0

Abstract

We prove the Wang transform inequality in every order: if nn is a positive integer, AA is a nonnegative n×nn\times n matrix whose row and column sums equal one, and JnJ_n has every entry 1/n1/n, then per⁡A≥per⁡ ⁣(nJn+An+1)\operatorname{per}A\ge \operatorname{per}\!\left(\frac{nJ_n+A}{n+1}\right). Equality holds exactly when A=JnA=J_n. We also obtain an explicit positive quadratic gap for every n≥2n\ge2.

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References

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Version history

  1. v1 · 4 pagesSubmitted by Yair LaviInitial depositCurrentNov 10, 2026