Results 141 to 150 of about 887,847 (298)
Baxter Algebras and Differential Algebras [PDF]
Differential Algebra and Related Topics, World Scientific
Publishing Company, 2002, 281-305, 2004 A Baxter algebra is a commutative algebra $A$ that carries a generalized integral operator. In the first part of this paper we review past work of Baxter, Miller, Rota and Cartier in this area and explain more recent work on explicit constructions of free Baxter algebras that extended the constructions of Rota and Cartier.
arxiv
Cubic algebras and Implication Algebras [PDF]
arXiv, 2009 We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra and the connection between these two operations.
arxiv
arXiv, 2004 Two important generalizations of the Hopf algebra of symmetric functions are the Hopf algebra of noncommutative symmetric functions and its graded dual the Hopf algebra of quasisymmetric functions. A common generalization of the latter is the selfdual Hopf algebra of permutations (MPR Hopf algebra).
arxiv
Operads in algebraic combinatorics
, 2017 The main ideas developed in this habilitation thesis consist in endowing combinatorial objects (words, permutations, trees, Young tableaux, etc.) with operations in order to construct algebraic structures. This process allows, by studying algebraically the structures thus obtained (changes of bases, generating sets, presentations, morphisms ...
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Algebras, Graphs and Ordered Sets - ALGOS 2020 & the Mathematical Contributions of Maurice Pouzet. [PDF]
Order (Dordr), 2023 Couceiro M, Duffus D.
europepmc +1 more source
Drinfeld Orbifold Algebras [PDF]
arXiv, 2011 We define Drinfeld orbifold algebras as filtered algebras deforming the skew group algebra (semi-direct product) arising from the action of a finite group on a polynomial ring. They simultaneously generalize Weyl algebras, graded (or Drinfeld) Hecke algebras, rational Cherednik algebras, symplectic reflection algebras, and universal enveloping algebras
arxiv
On the combinatorics of crystal structures. II. Number of Wyckoff sequences of a given subdivision complexity. [PDF]
Acta Crystallogr A Found Adv, 2023 Hornfeck W, Červený K.
europepmc +1 more source
Combinatorics of rooted trees and Hopf algebras [PDF]
Transactions of the American Mathematical Society, 2003 We begin by considering the graded vector space with a basis consisting of rooted trees, with grading given by the count of non-root vertices. We define two linear operators on this vector space, the growth and pruning operators, which respectively raise and lower grading; their commutator is the operator that multiplies a rooted tree by its number of ...
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The linear framework II: using graph theory to analyse the transient regime of Markov processes. [PDF]
Front Cell Dev Biol, 2023 Nam KM, Gunawardena J.
europepmc +1 more source
arXiv, 2007 We construct algebras from rhombohedral tilings of Euclidean space obtained as projections of certain cubical complexes. We show that these `Cubist algebras' satisfy strong homological properties, such as Koszulity and quasi-heredity, reflecting the combinatorics of the tilings.
arxiv