Canonical forms for dihedral and symmetric groups. (English) Zbl 1431.05151
Summary: 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.
MSC:
| 05E16 | Combinatorial aspects of groups and algebras |
| 06F15 | Ordered groups |
| 20B05 | General theory for finite permutation groups |
| 20B20 | Multiply transitive finite groups |
| 20B30 | Symmetric groups |
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