Jennifer Wagner, University of California, San Diego
TITLE:
Connections Between Symmetric Functions and Permutation Statistics
Abstract
Brenti introduced a homomorphism from the space of symmetric functions to
polynomials in one variable, which when applied to appropriate bases of
the space, gives generating functions for certain statistics on
permutations. I will give a combinatorial proof, due to Beck and Remmel,
of the fact that when the homomorphism is applied to the homogeneous basis
of the symmetric functions, the result is the well-known Euler polynomial,
the generating function for descents of a permutation. I will also
indicate how similar methods can be used to find other generating
functions for permuation statistics, and how the methods can be used to
find analogs for signed permutations.
R E F R E S H M E N T S
4:10 To 4:35 PM
Kenneth W. Anderson
Memorial Reading Room
