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The Kopotun Subpermanent Transform Inequality

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Contributed by Yair Lavi ↗

Version 1 / Nov 10, 2026 / CC BY 4.0

Abstract

We prove the subpermanent transform inequality conjectured by Kopotun in 1996: for every doubly stochastic matrix AA of order n≥2n\ge2 and every 2≤k≤n2\le k\le n, σk(A)≥σk((nJn+A)/(n+1))\sigma_k(A)\ge\sigma_k((nJ_n+A)/(n+1)). Here σk\sigma_k is the sum of all subpermanents of order kk, and JnJ_n has every entry 1/n1/n. Equality holds exactly at A=JnA=J_n.

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References

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Version history

  1. v1 · 13 pagesSubmitted by Yair LaviInitial depositCurrentNov 07, 2026