Recipe theorem for the Tutte polynomial for matroids,renormalization group-like approach |
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Authors: | Gérard HE Duchamp Nguyen Hoang-Nghia Thomas Krajewski Adrian Tanasa |
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Institution: | 1. Université Paris 13, Sorbonne Paris Cité, 99, avenue Jean-Baptiste Clément, LIPN, Institut Galilé, CNRS UMR 7030, F-93430, Villetaneuse, France;2. Centre de Physique Théorique, Campus de Luminy, Case 907, 13288 Marseille Cedex 9, France;3. Horia Hulubei National Institute for Physics and Nuclear Engineering, P.O.B. MG-6, 077125 Magurele, Romania |
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Abstract: | 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, V. Reiner, D. Stanton, A convolution formula for the Tutte polynomial, J. Combin. Theory Ser. B 76 (1999) 297–300] and G. Etienne, M. Las Vergnas, External and internal elements of a matroid basis, Discrete Math. 179 (1998) 111–119]. |
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Keywords: | 05B35 05E40 05E99 81T17 |
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