Orbifold Euler characteristics and the number of commuting n-tuples in symmetric groups

Details Orbifold Euler characteristics and the number of commuting n-tuples in symmetric groups Orbifold Euler characteristics and the number of commuting n-tuples in symmetric groups

1997-12-13

arxiv.org/abs/math/9712248v1

Mathematics

Combinatorics

Scientific paper

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.

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