Results 91 to 100 of about 131 (118)
Natural language syntax complies with the free-energy principle. [PDF]
SyntheseMurphy E, Holmes E, Friston K.
europepmc +1 more source
Deformations of combinatorial Hopf algebras and noncommutative Lagrange inversion
, 2011 This thesis is devoted to study one-parameter families of coproducts on symmetric functionsand their noncommutative analogues. We show, by introducing an appropriate basis,that a one-parameter family of Hopf algebras introduced by Foissy interpolates between theFa`a di Bruno algebra and the Farahat-Higman algebra.
openaire +1 more source
Commutative combinatorial Hopf algebras [PDF]
Journal of Algebraic Combinatorics, 2007 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 graphs, and its non-commutative dual is realized in three different ways, in particular as the ...
Florent Hivert +2 more
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Combinatorial Hopf Algebras and Towers of Algebras—Dimension, Quantization and Functorality [PDF]
Algebras and Representation Theory, 2010 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 endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and independently Lam and Shimozono constructed dual graded graphs from primitive elements in Hopf algebras.
Nantel Bergeron +2 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.
Florent Hivert +2 more
exaly +5 more sources
Combinatorial Hopf algebras from renormalization [PDF]
Journal of Algebraic Combinatorics, 2010 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 of the charge renormalization Hopf algebra on planar binary trees for quantum electrodynamics, and ...
Christian Brouder, Alessandra Frabetti
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Trees, functional equations, and combinatorial Hopf algebras
European Journal of Combinatorics, 2008 One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in power series rings.
Florent Hivert +2 more
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Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras [PDF]
Journal of Algebraic Combinatorics, 2011 We develop a theory of multigraded (i.e., $N^l$-graded) combinatorial Hopf algebras modeled on the theory of graded combinatorial Hopf algebras developed by Aguiar, Bergeron, and Sottile [Compos. Math. 142 (2006), 1--30]. In particular we introduce the notion of canonical $k$-odd and $k$-even subalgebras associated with any multigraded combinatorial ...
Samuel K Hsiao +2 more
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