The Tutte polynomial of a morphism of matroids - 5. Derivatives as generating functions of Tutte activities

Authors:
Michel Las Vergnas
Affiliations:
-
Venue:
European Journal of Combinatorics
Year:
2013

Citing 4
Cited 0

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Generalized activites and the Tutte polynomial

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Partitions of a finite Boolean lattice into intervals

European Journal of Combinatorics

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Abstract

We show that in an ordered matroid the partial derivative @?^p^+^qt/@?x^p@?y^q of the Tutte polynomial is p!q! times the generating function of activities of subsets with corank p and nullity q. More generally, this property holds for the 3-variable Tutte polynomial of a matroid perspective.