Pfaffian Formulas for Spanning Tree Probabilities
نویسندگان
چکیده
منابع مشابه
Chebyshev polynomials and spanning tree formulas for circulant and related graphs
Kirchhoo's Matrix Tree Theorem permits the calculation of the number of spanning trees in any given graph G through the evaluation of the determinant of an associated matrix. In the case of some special graphs Boesch and Prodinger 9] have shown how to use properties of Chebyshev polyno-mials to evaluate the associated determinants and derive closed formulas for the number of spanning trees of g...
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SCOTT HIRSCHMAN AND VICTOR REINER Kir ho 's elebrated Matrix-Tree Theorem gives a determinant ounting spanning trees in a graph. It has at least three di erent well-known proofs: one via the Binet-Cau hy Theorem (see e.g. [5, x2.2℄), one via a deletionontra tion indu tion (see e.g. [2, x13.2℄), and one due to Chaiken [1℄ via a sign-reversing involution. Re ently Masbaum and Vaintrob [3℄ proved ...
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This first algorithm is quite simple. (Though this was probably known earlier, its proof can be found in Prof. Indyk’s 1999 paper “Sublinear Time Algorithms for Metric Space Problems”.) Let Dij denote the distance between a pair of points i and j, over m total points. The entries of Dij must satisfy the triangle inequality; additionally the matrix is symmetric. Note that the matrix size (i.e., ...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2016
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548316000183