A Generalization of an Alternating Sum Formula for Finite Coxeter Groups

Details A Generalization of an Alternating Sum Formula for Finite Coxeter Groups A Generalization of an Alternating Sum Formula for Finite Coxeter Groups

1998-02-03

arxiv.org/abs/math/9802016v1

Mathematics

Group Theory

6 pages

Scientific paper

For W a finite Coxeter group, a formula is found for the size of W
equivalence classes of subsets of a base. The proof is a case-by-case analysis
using results and tables of Carter and Orlik/Solomon. As a corollary we obtain
an alternating sum identity which generalizes a well-known identity from the
theory of Coxeter groups.

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