A Generalization of an Alternating Sum Formula for Finite Coxeter Groups

1998/02/03 by Jason Fulman, Fulman, Jason
Mathematics · #20F55 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR #msc:20F55

paper · pdf · doi:10.48550/arxiv.math/9802016

6 pages

arxiv created 1998/02/03 · openalex publication_date 1998/02/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Alternating subgroups of Coxeter groups
• Generator Sets for the Alternating Group
• How large is the character degree sum compared to the character table sum for a finite group?
• Generalization of the basis theorem for alternating groups
• Some power series involving involutions in Coxeter groups