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A counterexample to the Foregger-Sinkhorn tie-point conjecture

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Contributed by Yair Lavi ↗

Version 1 / Nov 12, 2026/ arXiv: 2608.13025 / CC BY 4.0

Abstract

The Foregger-Sinkhorn tie-point conjecture asserts that if a nearly decomposable doubly stochastic matrix minimizes the permanent on a face and the permanental cofactor at a prescribed zero is larger than its permanent, then that zero is a tie point. We give a counterexample in dimension eight.

Tools used

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GPT-5.6-sol
Anthropic
Claude FableVersion 5

References

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Version history

  1. v1 · 10 pagesSubmitted by Yair LaviInitial depositCurrentNov 11, 2026