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– S. Carnahan ♦2010-06-14 16:14:53 +00:00Commented 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.
