Results 11 to 20 of about 3,007,169 (162)
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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A Combinatorial Perspective on the Noncommutative Symmetric Functions [PDF]
The Electronic Journal of CombinatoricsThe noncommutative symmetric functions $\textbf{NSym}$ were first defined abstractly by Gelfand et al. in 1995 as the free associative algebra generated by noncommuting indeterminates $\{\boldsymbol{e}_n\}_{n\in \mathbb{N}}$ that were taken as a noncommutative analogue of the elementary symmetric functions.
Angela Hicks, Robert McCloskey
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Noncommutative symmetric functions and an amazing matrix [PDF]
Advances in Applied Mathematics, 2012 6 ...
Novelli, Jean-Christophe +1 more
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On the Hopf Algebra of Noncommutative Symmetric Functions in Superspace
The Electronic Journal of Combinatorics, 2022 We study the combinatorial Hopf algebra of noncommutative symmetric functions in superspace sNSym, introduced by Fishel, Lapointe and Pinto. We introduce a family of primitive elements of sNSym and extend the noncommutative elementary and power sum functions to superspace. Then, we give formulas relating these families of functions.
Diego Arcis +2 more
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Grothendieck Bialgebras, Partition Lattices, and Symmetric Functions in Noncommutative Variables [PDF]
The Electronic Journal of Combinatorics, 2006 We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative variables. In particular this isomorphism singles out a canonical new basis of the symmetric functions in noncommutative variables which would be an analogue of the Schur ...
Nantel Bergeron +3 more
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Noncommutative Symmetric Bessel Functions
Canadian Mathematical Bulletin, 2008 AbstractThe consideration of tensor products of 0-Hecke algebramodules leads to natural analogs of the BesselJ-functions in the algebra of noncommutative symmetric functions. This provides a simple explanation of various combinatorial properties of Bessel functions.
Novelli, Jean-Christophe +1 more
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Differential operator specializations of noncommutative symmetric functions [PDF]
Advances in Mathematics, 2007 Let $K$ be any unital commutative $\mathbb Q$-algebra and $z=(z_1, ..., z_n)$ commutative or noncommutative free variables. Let $t$ be a formal parameter which commutes with $z$ and elements of $K$. We denote uniformly by $\kzz$ and $\kttzz$ the formal power series algebras of $z$ over $K$ and $K[[t]]$, respectively.
Zhao, Wenhua
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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 AND W-POLYNOMIALS [PDF]
Journal of Algebra and Its Applications, 2007 Let K, S, D be a division ring, an endomorphism and a S-derivation of K, respectively. In this setting we introduce generalized noncommutative symmetric functions and obtain Viète formula and decompositions of differential operators. W-polynomials show up naturally, their connections with P-independency, Vandermonde and Wronskian matrices are briefly ...
Delenclos, Jonathan, Leroy, André
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A Chromatic Symmetric Function in Noncommuting Variables [PDF]
Journal of Algebraic Combinatorics, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gebhard, David D., Sagan, Bruce E.
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