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Sign-Coherent Identities for Characteristic Polynomials of Matroids

Published online by Cambridge University Press:  12 September 2008

Joseph P. S. Kung
Joseph P. S. Kung
Affiliation:
Department of Mathematics, University of North Texas, Denton, Texas 76203, U.S.A.
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Abstract

We derive an explicit formula for the difference χ(G;λ) − χ(G|X;λ)χ(Tx(G); λ)/(λ − 1), where χ(G;λ) is the characteristic polynomial of a simple matroid G, G|X is the restriction of G to a flat X in G, and Tx(G) is the complete principal truncation of G at the flat X. Two counting proofs of this formula are given. The first uses the critical problem and the second uses the broken-circuit complex. We also derive several inequalities involving Whitney numbers of the first kind and other numerical invariants.

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Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 2 , Issue 1 , March 1993 , pp. 33 - 51
Copyright
Copyright © Cambridge University Press 1993

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