Results 21 to 30 of about 28,962 (144)
Tridendriform structure on combinatorial Hopf algebras [PDF]
Journal of Algebra, 2009 We extend the definition of tridendriform bialgebra by introducing a weight q. The subspace of primitive elements of a q-tridendriform bialgebra is equipped with an associative product and a natural structure of brace algebra, related by a distributive law. This data is called q-Gerstenhaber-Voronov algebras.
E. Burgunder, Maria O. Ronco
semanticscholar +8 more sources
Trees, functional equations, and combinatorial Hopf algebras [PDF]
European Journal of Combinatorics, 2007 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.
F. Hivert, J. Novelli, J. Thibon
semanticscholar +5 more sources
Combinatorial Hopf algebras from representations of families of wreath products [PDF]
Algebraic Combinatorics, 2020 We construct Hopf algebras whose elements are representations of combinatorial automorphism groups, by generalising a theorem of Zelevinsky on Hopf algebras of representations of wreath products.
Tyrone Crisp, C. Hill
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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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Mould calculus, polyhedral cones, and characters of combinatorial Hopf algebras [PDF]
Advances in Applied Mathematics, 2011 We describe a method for constructing characters of combinatorial Hopf algebras by means of integrals over certain polyhedral cones. This is based on ideas from resurgence theory, in particular on the construction of well-behaved averages induced by diffusion processes on the real line.
Frédéric Menous, J. Novelli, J. Thibon
semanticscholar +3 more sources
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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Combinatorial Hopf algebras, noncommutative Hall–Littlewood functions, and permutation tableaux [PDF]
Advances in Mathematics, 2008 37 pages, 4 figures, new references ...
J. Novelli, J. Thibon, L. Williams
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