G. Duchamp ; N. Hoang-Nghia ; Thomas Krajewski ; A. Tanasa - Renormalization group-like proof of the universality of the Tutte polynomial for matroids

dmtcs:12821 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.12821
Renormalization group-like proof of the universality of the Tutte polynomial for matroidsArticle

Authors: G. Duchamp 1; N. Hoang-Nghia 1; Thomas Krajewski ORCID2; A. Tanasa 1,3

  • 1 Laboratoire d'Informatique de Paris-Nord
  • 2 Centre de Physique Théorique - UMR 7332
  • 3 Horia Hulubei National Institute of Physics and Nuclear Engineering

In this paper we give a new proof of the universality of the Tutte polynomial for matroids. This proof uses appropriate characters of Hopf algebra of matroids, algebra introduced by Schmitt (1994). We show that these Hopf algebra characters are solutions of some differential equations which are of the same type as the differential equations used to describe the renormalization group flow in quantum field theory. This approach allows us to also prove, in a different way, a matroid Tutte polynomial convolution formula published by Kook, Reiner and Stanton (1999). This FPSAC contribution is an extended abstract.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Tutte polynomial for matroids,Hopf algebras for matroids,Hopf algebra characters,matroid recipe theorem,Combinatorial Physics,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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