Results 21 to 30 of about 20,221 (160)
Noncommutative Shifted Symmetric Functions [PDF]
Moscow Mathematical Journal, 2020 We introduce a ring of noncommutative shifted symmetric functions based on an integer-indexed sequence of shift parameters. Using generating series and quasideterminants, this multiparameter approach produces deformations of the ring of noncommutative symmetric functions.
Laugwitz, Robert, Retakh, Vladimir
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Symmetric functions in noncommuting variables [PDF]
Transactions of the American Mathematical Society, 2004 Consider the algebra Q<> of formal power series in countably many noncommuting variables over the rationals. The subalgebra Pi(x_1,x_2,...) of symmetric functions in noncommuting variables consists of all elements invariant under permutation of the variables and of bounded degree.
Rosas Celis, Mercedes Helena +1 more
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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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Noncommutative Symmetric Functions II: Transformations of Alphabets [PDF]
International Journal of Algebra and Computation, 1997 Noncommutative analogues of classical operations on symmetric functions are investigated, and applied to the description of idempotents and nilpotents in descent algebras. It is shown that any sequence of Lie idempotents (one in each descent algebra) gives rise to a complete set of indecomposable orthogonal idempotents of each descent algebra, and ...
Krob, Daniel +2 more
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Noncommutative Symmetrical Functions
Advances in Mathematics, 1995 This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables. This allows us to endow the resulting algebra with a Hopf structure, which leads to a new method for computing in ...
Gelfand, Israel M. +5 more
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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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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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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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Chromatic symmetric functions in noncommuting variables revisited [PDF]
Advances in Applied Mathematics, 2020 23 pages, final version to appear Adv.
Dahlberg, Samantha +1 more
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