Results 31 to 40 of about 336 (128)
Advances in Difference Equations, 2020 Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators ...
Rabha W. Ibrahim +2 more
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Unital versions of the higher order peak algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We construct unital extensions of the higher order peak algebras defined by Krob and the third author in [Ann. Comb. 9 (2005), 411―430], and show that they can be obtained as homomorphic images of certain subalgebras of the Mantaci-Reutenauer algebras of
Marcelo Aguiar +2 more
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NONCOMMUTATIVE SYMMETRIC FUNCTIONS AND THE INVERSION PROBLEM [PDF]
International Journal of Algebra and Computation, 2008 Let K be any unital commutative ℚ-algebra and z = (z1, z2, …, zn) commutative or noncommutative variables. Let t be a formal central parameter and K[[t]]〈〈z〉〉 the formal power series algebra of z over K[[t]]. In [29], for each automorphism Ft(z) = z - Ht(z) of K[[t]]〈〈z〉〉 with Ht=0(z) = 0 and o(H(z)) ≥ 1, a [Formula: see text] (noncommutative symmetric)
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Card-Shuffling via Convolutions of Projections on Combinatorial Hopf Algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Recently, Diaconis, Ram and I created Markov chains out of the coproduct-then-product operator on combinatorial Hopf algebras. These chains model the breaking and recombining of combinatorial objects.
C. Y. Amy Pang
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Colored Trees and Noncommutative Symmetric Functions [PDF]
The Electronic Journal of Combinatorics, 2010 Let ${\cal CRF}_S$ denote the category of $S$-colored rooted forests, and H$_{{\cal CRF}_S}$ denote its Ringel-Hall algebra as introduced by Kremnizer and Szczesny. We construct a homomorphism from a $K^+_0({\cal CRF}_S)$–graded version of the Hopf algebra of noncommutative symmetric functions to H$_{{\cal CRF}_S}$. Dualizing, we obtain a homomorphism
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Acyclic Complexes Related to Noncommutative Symmetric Functions [PDF]
Journal of Algebraic Combinatorics, 1997 Nous introduisons une famille de complexes acycliques sur l'algèbre des fonctions symétriques non commutatives.
Bergeron, François, Krob, Daniel
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Noncommutative symmetric functions and Lagrange inversion
Advances in Applied Mathematics, 2008 22 pages, 8 figures ...
Novelli, Jean-Christophe +1 more
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The Polarization Theorem and Polynomial Identities for Matrix Functions
Известия Иркутского государственного университета: Серия "Математика", 2017 In this article the simple combinatorial proof of the known polarization theorem (about the restoration of a polyadditive symmetric function over its values on a diagonal) is given.
G.P. Egorychev
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NONCOMMUTATIVE SYMMETRIC FUNCTIONS VI: FREE QUASI-SYMMETRIC FUNCTIONS AND RELATED ALGEBRAS [PDF]
International Journal of Algebra and Computation, 2002 This article is devoted to the study of several algebras related to symmetric functions, which admit linear bases labelled by various combinatorial objects: permutations (free quasi-symmetric functions), standard Young tableaux (free symmetric functions) and packed integer matrices (matrix quasi-symmetric functions).
Duchamp, G. +2 more
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Hasse-Schmidt Derivations and the Hopf Algebra of Non-Commutative Symmetric Functions
Axioms, 2012 Let NSymm be the Hopf algebra of non-commutative symmetric functions (in an infinity of indeterminates): . It is shown that an associative algebra A with a Hasse-Schmidt derivation ) on it is exactly the same as an NSymm module algebra. The primitives of
Michiel Hazewinkel
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