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Las Vergnas, Michel
The Tutte polynomial of a morphism of matroids I. Set-pointed matroids and matroid perspectives. Annales de l'institut Fourier, 49 no. 3 (1999), p. 973-1015
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Abstract

We study the basic algebraic properties of a 3-variable Tutte polynomial the author has associated with a morphism of matroids, more precisely with a matroid strong map, or matroid perspective in the present paper, or, equivalently by the Factorization Theorem, with a matroid together with a distinguished subset of elements. Most algebraic properties of the usual 2-variable Tutte polynomial of a matroid generalize to the 3-variable polynomial. Among specific properties we show that the 3-variable Tutte polynomial of a matroid $M$ pointed by a normal subset can be used to abridge the computation of the 2-variable Tutte polynomial of $M$, and that the 3-variable Tutte polynomial of a matroid perspective $M\rightarrow M'$ is computationally equivalent to the $r(M)-r(M')+1$ two-variable Tutte polynomials of the matroids of its Higgs factorization.

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