Abstract:
Generating functions for the number of commuting m-tuples in the symmetric
groups are obtained. We define a natural sequence of ``orbifold Euler
characteristics'' for a finite group G acting on a manifold X. Our
definition generalizes the ordinary Euler characteristic of X/G and the
string-theoretic orbifold Euler characteristic. Our formulae for commuting
m-tuples underlie formulas that generalize the results of Macdonald and
Hirzebruch-Hofer concerning the ordinary and string-theoretic Euler
characteristics of symmetric products.