Weiming Zhang

math.CO — Combinatorics

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

Contributed by Weiming Zhang

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