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Article Dans Une Revue Advances in Applied Mathematics Année : 2013

Recipe theorem for the Tutte polynomial for matroids, renormalization group-like approach

Résumé

Using a quantum field theory renormalization group-like differential equation, we give a new proof of the recipe theorem for the Tutte polynomial for matroids. The solution of such an equation is in fact given by some appropriate characters of the Hopf algebra of isomorphic classes of matroids, characters which are then related to the Tutte polynomial for matroids. This Hopf algebraic approach also allows to prove, in a new way, a matroid Tutte polynomial convolution formula appearing in W. Kook {\it et. al., J. Comb. Series} {\bf B 76} (1999).

Dates et versions

hal-01224286 , version 1 (04-11-2015)

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Gérard H. E. Duchamp, Nguyen Hoang-Nghia, Thomas Krajewski, Adrian Tanasa. Recipe theorem for the Tutte polynomial for matroids, renormalization group-like approach. Advances in Applied Mathematics, 2013, 51 (03), pp.345-358. ⟨10.1016/j.aam.2013.04.006⟩. ⟨hal-01224286⟩
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