# When is a triangular matrix totally unimodular?

I have an {0,1}, invertible, triangular matrix, that I would like to show to be totally unimodular. Are there any known results on the total unimodularity of classes of triangular matrices?

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There is a sufficient condition on the "unimodular" wikipedia page, but I don't know anything beyond that. – S. Carnahan Jun 14 '10 at 16:14

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.

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