Results 31 to 40 of about 7,293 (133)
Coloring Rings in Species [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We present a generalization of the chromatic polynomial, and chromatic symmetric function, arising in the study of combinatorial species. These invariants are defined for modules over lattice rings in species.
Jacob White
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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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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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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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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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Combinatorial Hopf Algebras and K-Homology of Grassmanians [PDF]
International Mathematics Research Notices, 2010 Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, we study six combinatorial Hopf algebras. These Hopf algebras can be thought of as K-theoretic analogues of the by now classical ``square'' of Hopf algebras consisting of symmetric functions, quasisymmetric functions, noncommutative symmetric functions and
Lam, Thomas, Pylyavskyy, Pavlo
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, 2008 The second part, dealing with right-sided combinatorial Hopf algebras, has been completely modified in this new ...
Loday, Jean-Louis, Ronco, Maria O.
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Coloured peak algebras and Hopf algebras [PDF]
, 2005 For $G$ a finite abelian group, we study the properties of general equivalence relations on $G_n=G^n\rtimes \SG_n$, the wreath product of $G$ with the symmetric group $\SG_n$, also known as the $G$-coloured symmetric group.
A. Björner +16 more
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Combinatorial Hopf algebras in noncommutative probabilility
, 2020 We prove that the generalized moment-cumulant relations introduced in [arXiv:1711.00219] are given by the action of the Eulerian idempotents on the Solomon-Tits algebras, whose direct sum builds up the Hopf algebra of Word Quasi-Symmetric Functions $\WQSym$.
Lehner, Franz +2 more
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A combinatorial non-commutative Hopf algebra of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Combinatorics A non-commutative, planar, Hopf algebra of planar rooted trees was defined independently by one of the authors in Foissy (2002) and by R. Holtkamp in Holtkamp (2003). In this paper we propose such a non-commutative Hopf algebra for graphs. In order to define a non-commutative product we use a quantum field theoretical (QFT) idea,
Duchamp, Gerard +4 more
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