A poset structure on the alternating group generated by 3-cycles
H M�hle, P Nadeau�- Algebraic Combinatorics, 2019 - numdam.org
H M�hle, P Nadeau
Algebraic Combinatorics, 2019•numdam.orgWe 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, ie 2-cycles, and we compare our results to this case along the
way. In particular, noncrossing partitions arise naturally in both settings.
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, ie 2-cycles, and we compare our results to this case along the
way. In particular, noncrossing partitions arise naturally in both settings.
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, ie 2-cycles, and we compare our results to this case along the way. In particular, noncrossing partitions arise naturally in both settings.
numdam.org