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The Equivalence of Two Graph Polynomials and a Symmetric Function

Published online by Cambridge University Press:  01 July 2009

CRIEL MERINO  and
STEVEN D. NOBLE
CRIEL MERINO
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Científica, Circuito Exterior, CU Coyoacán 04510, México, DF México (e-mail: merino@matem.unam.mx)
STEVEN D. NOBLE
Affiliation:
Department of Mathematical Sciences, Brunel University, Kingston Lane, Uxbridge, UB8 3PH, UK (e-mail: steven.noble@brunel.ac.uk)
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Abstract

The U-polynomial, the polychromate and the symmetric function generalization of the Tutte polynomial, due to Stanley, are known to be equivalent in the sense that the coefficients of any one of them can be obtained as a function of the coefficients of any other. The definition of each of these functions suggests a natural way in which to strengthen them, which also captures Tutte's universal V-function as a specialization. We show that the equivalence remains true for the strong functions, thus answering a question raised by Dominic Welsh.

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 18 , Issue 4 , July 2009 , pp. 601 - 615
Copyright
Copyright © Cambridge University Press 2009

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