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Coboundaries, Flows, and Tutte Polynomials of Matrices
Joseph P. S. Kung
Department of Mathematics, University of North Texas, P.O. Box 311430, Denton TX 76203, USA
kung@unt.edu
Annals of Combinatorics 12 (2) p.183-194 June, 2008
AMS Subject Classification: 05B35, 05C10
Abstract:
Using matroid duality and the critical problem, we show that certain evaluations of the Tutte polynomial of a matroid represented as a matrix over a finite field $\mathrm{GF}(q)$ can be interpreted as weighted sums over pairs $f,\,g$ of functions defined from the ground set to $\mathrm{GF}(q)$ whose difference $f-g$ is the restriction of a linear functional on the column
space of the matrix. Similar interpretations are given for the characteristic polynomial evaluated at $q$. These interpretations extend and elaborate interpretations for Tutte and chromatic polynomials of graphs due to Goodall and Matiyasevich.
Keywords: flows, Tutte polynomials, chromatic polynomials

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