Results 11 to 20 of about 20,221 (160)
A Noncommutative Cycle Index and New Bases of Quasi-symmetric Functions and Noncommutative Symmetric Functions [PDF]
Annals of Combinatorics, 2020 We define a new basis of the algebra of quasi-symmetric functions by lifting the cycle-index polynomials of symmetric groups to noncommutative polynomials with coefficients in the algebra of free quasi-symmetric functions, and then projecting the coefficients to $QSym$.
Novelli, Jean-Christophe +2 more
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Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited [PDF]
Annals of Combinatorics, 2008 We prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed.Comment: 21 pages, Latex, 2 ...
Duchamp, Gerard H. E. +3 more
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Noncommutative symmetric functions and W-polynomials [PDF]
Journal of Algebra and Its Applications, 2006 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 Vieta formula and decompositions of differential operators.
Delenclos, J., Leroy, A.
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Noncommutative symmetric functions and an amazing matrix
Advances in Applied Mathematics, 2012 6 ...
Novelli, Jean-Christophe +1 more
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Noncommutative symmetric functions and Laplace operators for classical Lie algebras [PDF]
Letters in Mathematical Physics, 1994 New systems of Laplace (Casimir) operators for the orthogonal and symplectic Lie algebras are constructed. The operators are expressed in terms of paths in graphs related to matrices formed by the generators of these Lie algebras with the use of some ...
A. M. Perelomov +9 more
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Noncommutative Schur functions, switchboards, and Schur positivity
Selecta Mathematica, New Series, 2016 The machinery of noncommutative Schur functions provides a general tool for obtaining Schur expansions for combinatorially defined symmetric functions. We extend this approach to a wider class of symmetric functions, explore its strengths and limitations,
Blasiak, Jonah, Fomin, Sergey
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Dual bases for noncommutative symmetric and quasi-symmetric functions via monoidal factorization
Journal of Symbolic Computation, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bui, V. C. +4 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
Bergeron, N. +3 more
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Noncommutative symmetric functions and skewing operators
Discrete MathematicsSkewing operators play a central role in the symmetric function theory because of the importance of the product structure of the symmetric function space. The theory of noncommutative symmetric functions is a useful tool for studying expansions of a given symmetric function in terms of various bases. In this paper, we establish a further development of
Byung-Hak Hwang
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