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An order-eleven counterexample to triangular realization of sign matrix permanents

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Contributed by Weiming Zhang ↗

Version 1 / Nov 13, 2026 / CC BY 4.0

Abstract

We construct an 11×1111\times11 sign matrix with permanent P=2 029 568P=2\,029\,568. An exhaustive enumeration shows that \(\lvert\per B\rvert\ne P\) for every sign matrix BB of order eleven whose entries below the diagonal are all +1+1. This gives a negative answer to a question of Ingram and Razborov.

References

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Version history

  1. v1 · 12 pagesSubmitted by Weiming ZhangInitial depositCurrentNov 13, 2026