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Some Inequalities for Whitney–Tutte Polynomials

Published online by Cambridge University Press:  11 December 2009

ARUN P. MANI
ARUN P. MANI*
Affiliation:
Clayton School of Information Technology, Monash University, Clayton VIC 3800, Australia (e-mail: arunpmani@gmail.com)
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Abstract

We introduce and prove a family of inequalities satisfied by the Whitney rank generating function of a matroid in the positive quadrant of ℝ2. These can be interpreted as correlation inequalities at those points where the polynomial is known to count the number of independent sets, bases or spanning sets of the matroid. Our proofs also introduce an idea of rank dominating bijections in matroids, which are then used to obtain some simple extensions of the submodular property of matroid ranks.

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 19 , Issue 3 , May 2010 , pp. 425 - 439
Copyright
Copyright © Cambridge University Press 2009

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