Coboundaries, Flows, and Tutte Polynomials of Matrices |
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Authors: | Joseph P S Kung |
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Institution: | (1) Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203, USA |
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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 GF(q) can be interpreted as weighted sums over pairs f , g of functions defined from the ground set to 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.
Received July 14, 2006 |
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Keywords: | :" target="_blank">: flows Tutte polynomials chromatic polynomials |
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