I have a {0,1}, invertible, triangular matrix, that I would like to show is totally unimodular. Are there any known results on the total unimodularity of classes of triangular matrices?
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$\begingroup$ There is a sufficient condition on the "unimodular" wikipedia page, but I don't know anything beyond that. $\endgroup$– S. Carnahan ♦Commented Jun 14, 2010 at 16:14
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Seymour's decomposition theorem for regular matroids yields a polynomial-time algorithm for testing if any {0,1,-1} matrix is totally unimodular. Unfortunately, due to the sound of paint drying on this question of Gordon Royle, it seems as if no one has yet implemented it.
answered Jun 14, 2010 at 17:37