๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Plethysm and conjugation of quasi-symmetric functions

โœ Scribed by Claudia Malvenuto; Christophe Reutenauer

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
415 KB
Volume
193
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

โœฆ Synopsis

Let Fc denote the basic quasi-symmetric functions, in Gessel's notation (1984) (C any composition). The plethysm sz oFc is a positive linear combination of functions Fo. Under certain conditions, the image under the involution ~o of a quasi-symmetric function defined by equalities and inequalities of the variables is obtained by negating the inequalities. (~)

๐Ÿ“œ SIMILAR VOLUMES

A Class of q-Symmetric Functions Arising
A Class of q-Symmetric Functions Arising from Plethysm
โœ Francesco Brenti ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 299 KB

We introduce and study a class of symmetric functions that depend on a parameter q, which includes symmetric functions that have already appeared in the literature in connection with Jack symmetric functions, parking functions, and lattices of noncrossing partitions. Our results generalize previous

Hecke Algebras, Difference Operators, an
Hecke Algebras, Difference Operators, and Quasi-Symmetric Functions
โœ Florent Hivert ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 470 KB

We define a new action of the symmetric group and its Hecke algebra on polynomial rings whose invariants are exactly the quasi-symmetric polynomials. We interpret this construction in terms of a Demazure character formula for the irreducible polynomial modules of a degenerate quantum group. We use t

The Algebra of Quasi-Symmetric Functions
The Algebra of Quasi-Symmetric Functions Is Free over the Integers
โœ Michiel Hazewinkel ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 144 KB

Let Z denote the Leibniz-Hopf algebra, which also turns up as the Solomon descent algebra and the algebra of noncommutative symmetric functions. As an algebra Z=ZOZ 1 , Z 2 , ...P, the free associative algebra over the integers in countably many indeterminates. The coalgebra structure is given by m(

Duality between Quasi-Symmetrical Functi
Duality between Quasi-Symmetrical Functions and the Solomon Descent Algebra
โœ C. Malvenuto; C. Reutenauer ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 650 KB

The ring QSym of quasi-symmetric functions is naturally the dual of the Solomon descent algebra. The product and the two coproducts of the first (extending those of the symmetric functions) correspond to a coproduct and two products of the second, which are defined by restriction from the symmetric