Results 1 to 10 of about 1,475 (226)
Ann Comb, 2022 AbstractIn this paper, we expand on the notion of combinatorial presheaf, first introduced explicitly by Aguiar and Mahajan in 2010 but already present in the literature in some other points of view. We do this by adapting the algebraic framework of species to the study of substructures in combinatorics. Afterwards, we consider functions that count the
Penaguiao R.
europepmc +5 more sources
A Hopf algebra of subword complexes (Extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acyclic orientations of certain graphs, and show that this Hopf algebra induces ...
Nantel Bergeron, Cesar Ceballos
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Centrification of algebras and Hopf algebras [PDF]
Canadian Mathematical Bulletin, 2021 AbstractWe investigate a method of construction of central deformations of associative algebras, which we call centrification. We prove some general results in the case of Hopf algebras and provide several examples.
Rumynin, Dmitriy, Westaway, Matthew
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Cofree Hopf algebras on Hopf bimodule algebras [PDF]
Journal of Pure and Applied Algebra, 2015 We investigate a Hopf algebra structure on the cotensor coalgebra associated to a Hopf bimodule algebra which contains universal version of Clifford algebras and quantum groups as examples. It is shown to be the bosonization of the quantum quasi-shuffle algebra built on the space of its right coinvariants.
Fang, Xin, Jian, Run-Qiang
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Baxter algebras and Hopf algebras [PDF]
Transactions of the American Mathematical Society, 2003 By applying a recent construction of free Baxter algebras, we obtain a new class of Hopf algebras that generalizes the classical divided power Hopf algebra. We also study conditions under which these Hopf algebras are isomorphic.
Andrews, George E. +3 more
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Discrete Mathematics & Theoretical Computer Science, 2014 A general lattice theoretic construction of Reading constructs Hopf subalgebras of the Malvenuto-Reutenauer Hopf algebra (MR) of permutations. The products and coproducts of these Hopf subalgebras are defined extrinsically in terms of the embedding in MR.
Shirley Law
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The Incidence Hopf Algebra of Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 The graph algebra is a commutative, cocommutative, graded, connected incidence Hopf algebra, whose basis elements correspond to finite simple graphs and whose Hopf product and coproduct admit simple combinatorial descriptions.
Brandon Humpert, Jeremy L. Martin
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Proceedings of the London Mathematical Society, 2001 50 pages, LaTeX ...
Vaes, Stefaan, Van Daele, Alphons
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Higher Structures, 2021 We introduce the notion of an oplax Hopf monoid in any braided monoidal bicategory, generalizing that of a Hopf monoid in a braided monoidal category in an appropriate way. We show that Hopf V-categories introduced in [BCV16] are a particular type of oplax Hopf monoids in the monoidal bicategory Span|V described in [Böh17].
Buckley, Mitchell +3 more
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