Results 1 to 10 of about 28,962 (144)
Combinatorial Hopf Algebras of Simplicial Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We consider a Hopf algebra of simplicial complexes and provide a cancellation-free formula for its antipode. We then obtain a family of combinatorial Hopf algebras by defining a family of characters on this Hopf algebra.
Carolina Benedetti +2 more
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Antipode Formulas for some Combinatorial Hopf Algebras [PDF]
The Electronic Journal of Combinatorics, 2015 Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, Lam and Pylyavskyy studied six combinatorial Hopf algebras that can be thought of as K-theoretic analogues of the Hopf algebras of symmetric functions ...
Rebecca Patrias
semanticscholar +6 more sources
Combinatorial Hopf algebras and generalized Dehn–Sommerville relations [PDF]
Compositio Mathematica, 2003 A combinatorial Hopf algebra is a graded connected Hopf algebra over a field $\Bbbk$ equipped with a character (multiplicative linear functional) $\zeta\colon{\mathcal H}\to \Bbbk$.
M. Aguiar, N. Bergeron, F. Sottile
semanticscholar +10 more sources
Commutative combinatorial Hopf algebras [PDF]
Journal of Algebraic Combinatorics, 2006 We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general construction based on
F. Hivert, J. Novelli, J. Thibon
semanticscholar +12 more sources
Combinatorial Hopf algebras in quantum field theory. I [PDF]
Reviews in Mathematical Physics, 2004 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.
H. Figueroa, J. Gracia-Bond́ıa
semanticscholar +7 more sources
Combinatorial Hopf algebras from renormalization [PDF]
Journal of Algebraic Combinatorics, 2009 In this paper we describe the right-sided combinatorial Hopf structure of three Hopf algebras appearing in the context of renormalization in quantum field theory: the non-commutative version of the Faà di Bruno Hopf algebra, the non-commutative version ...
C. Brouder +2 more
semanticscholar +17 more sources
Combinatorial Hopf algebras from PROs [PDF]
Journal of Algebraic Combinatorics, 2014 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.
Jean-Paul Bultel, Samuele Giraudo
semanticscholar +11 more sources
The # product in combinatorial Hopf algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We show that the # product of binary trees introduced by Aval and Viennot (2008) is in fact defined at the level of the free associative algebra, and can be extended to most of the classical combinatorial Hopf algebras.
Jean-Christophe Aval +2 more
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Combinatorial Hopf Algebras and Towers of Algebras—Dimension, Quantization and Functorality [PDF]
Algebras and Representation Theory, 2007 Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $\bigoplus_{n\ge0}A_n$ can be a pair of graded dual Hopf algebras.
N. Bergeron, T. Lam, Huilan Li
semanticscholar +12 more sources
Card-Shuffling via Convolutions of Projections on Combinatorial Hopf Algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Recently, Diaconis, Ram and I created Markov chains out of the coproduct-then-product operator on combinatorial Hopf algebras. These chains model the breaking and recombining of combinatorial objects.
C. Y. Amy Pang
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