Results 1 to 10 of about 131 (118)
Combinatorial Hopf Algebras and Towers of Algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $\bigoplus_{n \geq 0}A_n$ can be endowed with the structure of graded dual Hopf algebras.
Nantel Bergeron, Thomas Lam, Huilan Li
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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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Quasisymmetric functions from combinatorial Hopf monoids and Ehrhart Theory [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We investigate quasisymmetric functions coming from combinatorial Hopf monoids. We show that these invariants arise naturally in Ehrhart theory, and that some of their specializations are Hilbert functions for relative simplicial complexes. This class of
Jacob White
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Lattice of combinatorial Hopf algebras: binary trees with multiplicities [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 In a first part, we formalize the construction of combinatorial Hopf algebras from plactic-like monoids using polynomial realizations. Thank to this construction we reveal a lattice structure on those combinatorial Hopf algebras.
Jean-Baptiste Priez
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Algebraic and combinatorial structures on Baxter permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We give a new construction of a Hopf subalgebra of the Hopf algebra of Free quasi-symmetric functions whose bases are indexed by objects belonging to the Baxter combinatorial family (\emphi.e.
Samuele Giraudo
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Redfield-Pólya theorem in $\mathrm{WSym}$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We give noncommutative versions of the Redfield-Pólya theorem in $\mathrm{WSym}$, the algebra of word symmetric functions, and in other related combinatorial Hopf algebras.
Jean-Paul Bultel +3 more
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Convolution Powers of the Identity [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We study convolution powers $\mathtt{id}^{\ast n}$ of the identity of graded connected Hopf algebras $H$. (The antipode corresponds to $n=-1$.) The chief result is a complete description of the characteristic polynomial - both eigenvalues and ...
Marcelo Aguiar, Aaron Lauve
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The dynamics of non-perturbative phases via Banach bundles
Nuclear Physics B, 2021 Strongly coupled Dyson–Schwinger equations generate infinite power series of running coupling constants together with Feynman diagrams with increasing loop orders as coefficients. Theory of graphons for sparse graphs can address a new useful approach for
Ali Shojaei-Fard
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Partial categorification of Hopf algebras and representation theory of towers of \mathcalJ-trivial monoids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 This paper considers the representation theory of towers of algebras of $\mathcal{J} -trivial$ monoids. Using a very general lemma on induction, we derive a combinatorial description of the algebra and coalgebra structure on the Grothendieck rings $G_0 ...
Aladin Virmaux
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