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6 votes
2 answers
1k views

Determinant of the oriented adjacency matrix of a tree

Let $(V,E)$ be a finite oriented directed graph, with vertices and edges ordered, and $M$ the $|V|\times |E|$ matrix with entries $$ m_{ve} = \begin{cases} 1 &\text{if $e$ points at $v$}\\ -1 &...
3 votes
0 answers
105 views

Can one do better than using general purpose determinant algorithms when using the Fisher-Kasteleyn-Temperley method for perfect matchings?

Questions. (numerical.generalPfaffian) Is it proved anywhere that in general it is not easier0 to calculate the determinant (over $\mathbb{Q}$) of the skew-symmetric signed adjacency matrix defined ...