Coxeter groups are of central importance in several areas of algebra, geometry, and
combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of …

Publisher Summary This chapter explores that the Lie algebra of Lie polynomials is the free
Lie algebra. Lie polynomials appeared at the end of the 19th century and the beginning of …

Counting Permutations with Given Cycle Structure and Descent Set Page 1 JOURNAL OF
COMBINATORIAL THEORY, Series A 64, 189-215 (1993) Counting Permutations with …

The cyclic sieving phenomenon is defined for generating functions of a set affording a cyclic
group action, generalizing Stembridge's q=− 1 phenomenon. The phenomenon is shown to …

We introduce a new family of symmetric functions, which are q analogs of products of Schur
functions, defined in terms of ribbon tableaux. These functions can be interpreted in terms of …

Let G be a finite group. The eigenvalues of any g∈ G of order m in a (complex)
representation ρ may be expressed in the form ω e 1, ω e 2,…, with ω= e 2 πi∕ m. We call …

A new extension of the major index, defined in terms of Coxeter elements, is introduced. For
the classical Weyl groups of type B, it is equidistributed with length. For more general wreath …

Given an alphabet A={a 1, a 2… an}, the smallest subspace of the linear space of A-words,
which contains the words of length one and is closed under the bracket operation [f, g]= fg …

The cyclic sieving phenomenon was defined by Reiner, Stanton, and White in a 2004 paper.
Let X be a finite set, C be a finite cyclic group acting on X, and f (q) be a polynomial in q with …

This paper presents a survey of recent applications of Hall-Littlewood functions and Kostka-
Foulkes polynomials to the representation theory of the general linear group GL (n, C) and of …