Results 1 to 10 of about 336 (128)
Noncommutative symmetric functions with matrix parameters [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We define new families of noncommutative symmetric functions and quasi-symmetric functions depending on two matrices of parameters, and more generally on parameters associated with paths in a binary tree. Appropriate specializations of both matrices then
Alain Lascoux +2 more
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Noncommutative symmetric functions associated with a code, Lazard elimination, and Witt vectors [PDF]
Discrete Mathematics & Theoretical Computer Science, 2007 The construction of the universal ring of Witt vectors is related to Lazard's factorizations of free monoids by means of a noncommutative analogue. This is done by associating to a code a specialization of noncommutative symmetric functions.
Jean-Gabriel Luque, Jean-Yves Thibon
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Noncommutative symmetric functions III: Deformations of Cauchy and convolution algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 1997 This paper discusses various deformations of free associative algebras and of their convolution algebras. Our main examples are deformations of noncommutative symmetric functions related to families of idempotents in descent algebras, and a simple q-
Gérard H. E. Duchamp +3 more
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Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited [PDF]
Annals of Combinatorics, 2011 21 pages, Latex, 2 figuresInternational audienceWe prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases.
Gérard H E Duchamp +2 more
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Discrete Mathematics, 2010 34 pages; LaTEXInternational audienceWe introduce analogs of the Hopf algebra of Free quasi-symmetric functions with bases labelled by colored permutations. When the color set is a semigroup, an internal product can be introduced.
Jean-Christophe Novelli +1 more
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Noncommutative Symmetric Hall-Littlewood Polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Noncommutative symmetric functions have many properties analogous to those of classical (commutative) symmetric functions. For instance, ribbon Schur functions (analogs of the classical Schur basis) expand positively in noncommutative monomial basis ...
Lenny Tevlin
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Selecta Mathematica, New Series, 2009 International audienceWe prove conjectures of the third author [L. Tevlin, Proc. FPSAC'07, Tianjin] on two new bases of noncommutative symmetric functions: the transition matrices from the ribbon basis have nonnegative integral coefficients. This is done
Florent Hivert +2 more
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The Murnaghan―Nakayama rule for k-Schur functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We prove a Murnaghan–Nakayama rule for k-Schur functions of Lapointe and Morse. That is, we give an explicit formula for the expansion of the product of a power sum symmetric function and a k-Schur function in terms of k-Schur functions.
Jason Bandlow +2 more
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$0$-Hecke algebra action on the Stanley-Reisner ring of the Boolean algebra [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We define an action of the $0$-Hecke algebra of type A on the Stanley-Reisner ring of the Boolean algebra. By studying this action we obtain a family of multivariate noncommutative symmetric functions, which specialize to the noncommutative Hall ...
Jia Huang
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Redfield-Pólya theorem in $\mathrm{WSym}$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We give noncommutative versions of the Redfield-Pólya theorem in $\mathrm{WSym}$, the algebra of word symmetric functions, and in other related combinatorial Hopf algebras.
Jean-Paul Bultel +3 more
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