Results 21 to 30 of about 131 (118)
A polynomial realization of the Hopf algebra of uniform block permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Poster ...
Rémi Maurice
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Hopf Algebras of Combinatorial Structures [PDF]
Canadian Journal of Mathematics, 1993 AbstractA generalization of the definition of combinatorial species is given by considering functors whose domains are categories of finite sets, with various classes of relations as moronisms. Two cases in particular correspond to species for which one has notions of restriction and quotient of structures.
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Superization and $(q,t)$-Specialization in Combinatorial Hopf Algebras [PDF]
The Electronic Journal of Combinatorics, 2009 We extend a classical construction on symmetric functions, the superization process, to several combinatorial Hopf algebras, and obtain analogs of the hook-content formula for the $(q,t)$-specializations of various bases. Exploiting the dendriform structures yields in particular $(q,t)$-analogs of the Björner-Wachs $q$-hook-length formulas for binary ...
Novelli, Jean-Christophe +1 more
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Dendriform structures for restriction-deletion and restriction-contraction matroid Hopf algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 We endow the set of isomorphism classes of matroids with a new Hopf algebra structure, in which the coproduct is implemented via the combinatorial operations of restriction and deletion.
Nguyen Hoang-Nghia +2 more
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Tridendriform structure on combinatorial Hopf algebras
Journal of Algebra, 2010 We extend the definition of tridendriform bialgebra by introducing a weight q. The subspace of primitive elements of a q-tridendriform bialgebra is equipped with an associative product and a natural structure of brace algebra, related by a distributive law. This data is called q-Gerstenhaber-Voronov algebras.
Burgunder, Emily, Ronco, Maria
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Renormalization group-like proof of the universality of the Tutte polynomial for matroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 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
G. Duchamp +3 more
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COMBINATORIAL HOPF ALGEBRAS IN QUANTUM FIELD THEORY I [PDF]
Reviews in Mathematical Physics, 2005 This paper stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Sec. 1.1 is the introduction, and contains an elementary invitation to the subject as well. The rest of Sec. 1 is devoted to the basics of Hopf algebra theory and examples in ascending level of complexity.
Figueroa, Héctor +1 more
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r-Bell polynomials in combinatorial Hopf algebras
Comptes Rendus. Mathématique, 2017 We introduce partial r -Bell polynomials in three combinatorial Hopf algebras. We prove a factorization formula for the generating functions which is a consequence of the Zassenhauss formula.
Chouria, Ali, Luque, Jean-Gabriel
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Combinatorial Hopf algebras from PROs [PDF]
Journal of Algebraic Combinatorics, 2016 We introduce a general construction that takes as input a so-called stiff PRO and that outputs a Hopf algebra. Stiff PROs are particular PROs that can be described by generators and relations with precise conditions. Our construction generalizes the classical construction from operads to Hopf algebras of van der Laan.
Bultel, Jean-Paul, Giraudo, Samuele
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A Combinatorial Overview of the Hopf Algebra of MacMahon Symmetric Functions [PDF]
Annals of Combinatorics, 2002 A MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal action of the symmetric group. In this article, we give a combinatorial overview of the Hopf algebra structure of the MacMahon symmetric functions relying on the construction of a Hopf algebra from any alphabet of neutral letters ...
Rosas Celis, Mercedes Helena +2 more
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