Results 91 to 100 of about 133 (121)
Natural language syntax complies with the free-energy principle. [PDF]
SyntheseMurphy E, Holmes E, Friston K.
europepmc +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 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 +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, Thomas Lam, Huilan Li
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A combinatorial Hopf algebra on partition diagrams
Communications in AlgebraWe introduce a Combinatorial Hopf Algebra (CHA) with bases indexed by the partition diagrams indexing the bases for partition algebras. By analogy with the operation $H_α H_β = H_{α\cdot β}$ for the complete homogeneous basis of the CHA $ \textsf{NSym}$ given by concatenating compositions $α$ and $β$, we mimic this multiplication rule by setting ...
John M Campbell
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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 ...
Gizem Karaali, Samuel Khe-jin Hsiao
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Combinatorial Hopf algebra of superclass functions of type D [PDF]
Journal of Algebraic Combinatorics, 2013 Last section modified.
Carolina Benedetti
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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.
Samuele Giraudo
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