A Poset Structure on the Alternating Group Generated by 3-Cycles
arXiv:1803.00540 · doi:10.5802/alco.83
Abstract
We investigate the poset structure on the alternating group that arises when the latter is generated by 3-cycles. We study intervals in this poset and give several enumerative results, as well as a complete description of the orbits of the Hurwitz action on maximal chains. Our motivating example is the well-studied absolute order arising when the symmetric group is generated by transpositions, i.e. 2-cycles, and we compare our results to this case along the way. In particular, noncrossing partitions arise naturally in both settings.
29 pages, 2 figures, 3 tables, comments welcome. Final version
References in corpus (3)
Cited by in corpus (4)
- Connectivity Properties of Factorization Posets in Generated Groups
- -Indivisible Noncrossing Partitions
- Hurwitz Transitivity of Longer Reflection Factorizations in G4 and G5
- In which it is proven that, for each parabolic quasi-Coxeter element in a finite real reflection group, the orbits of the Hurwitz action on its reflection factorizations are distinguished by the two obvious invariants