454 research outputs found

    Hopf algebras: motivations and examples

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    This paper provides motivation as well as a method of construction for Hopf algebras, starting from an associative algebra. The dualization technique involved relies heavily on the use of Sweedler's dual

    Definite integrals and operational methods

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    An operatorial method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various type. This technique provide a very flexible and powerful tool yielding new results encompassing various aspects of the special function theory.Comment: 9 pages; minor changes to match published versio

    A localized version of the basic triangle theorem

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    In this short note, we give a localized version of the basic triangle theorem, first published in 2011 (see [4]) in order to prove the independence of hyperlogarithms over various function fields. This version provides direct access to rings of scalars and avoids the recourse to fraction fields as that of meromorphic functions for instance

    Le support de l'algebre de lie libre

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    AbstractWe characterize the words appearing as monomials in Lie polynomials

    Renormalization group-like proof of the universality of the Tutte polynomial for matroids

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    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.Comment: 12 pages, 3 figures, conference proceedings, 25th International Conference on Formal Power Series and Algebraic Combinatorics, Paris, France, June 201
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