Related papers: Noncommutative Symmetric Functions and an Amazing …
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.…
FPSAC 2013 Extended Abstract. We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build a basis of the quasi-symmetric functions which expand…
We define two-parameter families of noncommutative symmetric functions and quasi-symmetric functions, which appear to be the proper analogues of the Macdonald symmetric functions in these settings.
We introduce two families of non-commutative symmetric functions that have analogous properties to the Hall-Littlewood and Macdonald symmetric functions.
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
The noncommutative symmetric functions $\textbf{NSym}$ were first defined abstractly by Gelfand et al. in 1995 as the free associative algebra generated by noncommuting indeterminants $\{\boldsymbol{e}_n\}_{n\in \mathbb{N}}$ that were taken…
We investigate the connections between various noncommutative analogues of Hall-Littlewood and Macdonald polynomials, and define some new families of noncommutative symmetric functions depending on two sequences of parameters.
We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…
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…
We begin with an improvement to an extension result for subharmonic functions of Blanchet et al. With the aid of this improvement we then give extension results for subharmonic functions, for separately subharmonic functions, for harmonic…
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.…
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…
Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.
Noncommutative functions are graded functions between sets of square matrices of all sizes over two vector spaces that respect direct sums and similarities. They possess very strong regularity properties (reminiscent of the regularity…
The symmetric function theorem states that a polynomial that is invariant under permutation of variables, is a polynomial in the elementary symmetric polynomials. We deduce this classical result, in the analytic setting, from the…
This article is devoted to the study of several algebras which are related to symmetric functions, and which admit linear bases labelled by various combinatorial objects: permutations (free quasi-symmetric functions), standard Young…
This paper is concerned with two generalizations of the Hopf algebra of symmetric functions that have more or less recently appeared. The Hopf algebra of noncommutative symmetric functions and its dual, the Hopf algebra of quasisymmetric…
We introduce a new pair of mutually dual bases of noncommutative symmetric functions and quasi-symmetric functions, and use it to derive generalizations of several results on the reduced incidence algebra of the lattice of noncrossing…
The symmetric Macdonald polynomials are able to be constructed out of the non-symmetric Macdonald polynomials. This allows us to develop the theory of the symmetric Macdonald polynomials by first developing the theory of their non-symmetric…
In this paper, we prove Newton-Maclaurin type inequalities for functions obtained by linear combination of two neighboring primary symmetry functions, which is a generalization of the classical Newton-Maclaurin inequality.