Annals of Combinatorics 2 (1998) 1-6

Jim Bryan and Jason Fulman

Department of Mathematics,University of California, Berkeley, CA 94720, USA
jbryan@math.berkeley.edu

Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA
jason.e.fulman@dartmouth.edu

Received November 4, 1997

AMS Subject Classification: 55N20, 20B30

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 formulae that generalize the results of Macdonald and Hirzebruch-Höfer concerning the ordinary and string-theoretic Euler characteristics of symmetric products.

Keywords: Euler characteristic, orbifold, cohomology, symmetric groups

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