Results 41 to 50 of about 28,962 (144)
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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Affine Schubert classes, Schur positivity, and combinatorial Hopf algebras [PDF]
, 2009 We develop the point of view that Schubert classes of the affine Grassmannian of a simple algebraic group G can be identified with Schur‐positive symmetric functions.
T. Lam
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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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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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The $(1-\mathbb{E})$ -transform in combinatorial Hopf algebras [PDF]
Journal of Algebraic Combinatorics, 2010 Let sym be the commutative algebra of symmetric functions in countably infinite many variables \(x_1, x_2, \dots,\) \textbf{Sym} the non-commutative symmetric functions, \textbf{FQSym} the free quasi-symmetric functions, \textbf{WQSym} the word quasi-symmetric functions and \textbf{PQSym} the parking quasi-symmetric functions.
Hivert, Florent +3 more
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From left modules to algebras over an operad: application to combinatorial Hopf algebras [PDF]
, 2006 The purpose of this paper is two fold: we study the behaviour of the forgetful functor from S-modules to graded vector spaces in the context of algebras over an operad and derive the construction of combinatorial Hopf algebras.
M. Livernet
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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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