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Abstract Abdesselam [1] showed how the techniques of Grassmann-Berezin calculus can be used to prove the all-minors matrix-tree theorem. Starting with any matrix A we associate a directed graph G… Click to show full abstract
Abstract Abdesselam [1] showed how the techniques of Grassmann-Berezin calculus can be used to prove the all-minors matrix-tree theorem. Starting with any matrix A we associate a directed graph G to A equipped with two different weight functions on the edges. We extend the approach of Abdesselam to give interpretations for the permanents and determinants of all square sub-matrices of A in terms of weighted counts of sub-graphs of G using each of the edge-weight functions. We introduce a modification of Grassmann-Berezin variables to obtain our results.
Journal Title: Linear Algebra and its Applications
Year Published: 2019
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