The Equivalence of Two Graph Polynomials and a Symmetric Function

Details The Equivalence of Two Graph Polynomials and a Symmetric Function The Equivalence of Two Graph Polynomials and a Symmetric Function

2008-05-30

arxiv.org/abs/0805.4793v1

Mathematics

Combinatorics

17 pages

Scientific paper

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 generalize them which also captures Tutte's universal V-functions as a specialization. We show that the equivalence remains true for the extended functions thus answering a question raised by Dominic Welsh.

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