Complement minimally non-totally unimodular matrices
Suyoung Choi, Mathieu Vallée
Abstract
We prove that, up to row and column permutations and complement operations, the only complement minimally non-totally unimodular matrices are the cycle matrices C3 and C5. This settles a conjecture of Chervet, Grappe, and Vallée. As a consequence, every simplicial cone generated by the rows of a totally equimodular matrix admits a regular unimodular Hilbert triangulation.
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