In this paper we introduce the elementary factorization of the standard OGS for the symmetric group, and show how it encodes the inversion and descent set statistics. Proofs follow from exchange laws for powers of Coxeter elements in the principal flag.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics