TL;DR
This paper provides a uniform proof for Chapoton's product formula counting reflections with full support in Weyl groups and refines it based on root length, advancing understanding of Coxeter group structures.
Contribution
It offers a uniform proof of Chapoton's formula for Weyl groups and refines the count by root length, enhancing combinatorial understanding.
Findings
Proved Chapoton's formula uniformly for Weyl groups
Refined the formula by incorporating root length
Enhanced combinatorial understanding of Coxeter group reflections
Abstract
Chapoton has observed a simple product formula for the number of reflections in a finite Coxeter group that have full support. We give a uniform proof of his formula for Weyl groups. We furthermore refine his formula by the length of the roots.
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