# ALGEBRAIC COMBINATORICS

A poset structure on the alternating group generated by 3-cycles
Algebraic Combinatorics, Volume 2 (2019) no. 6, pp. 1285-1310.

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.

Revised: 2019-01-21
Accepted: 2019-04-29
Published online: 2019-12-04
DOI: https://doi.org/10.5802/alco.83
Classification: 06A07,  05A10,  05E15,  20B35
Keywords: Symmetric group, Alternating group, Noncrossing partitions, Hurwitz action, zeta polynomial
@article{ALCO_2019__2_6_1285_0,
author = {M\"uhle, Henri and Nadeau, Philippe},
title = {A poset structure on the alternating group generated by 3-cycles},
journal = {Algebraic Combinatorics},
publisher = {MathOA foundation},
volume = {2},
number = {6},
year = {2019},
pages = {1285-1310},
doi = {10.5802/alco.83},
mrnumber = {4049847},
language = {en},
url = {alco.centre-mersenne.org/item/ALCO_2019__2_6_1285_0/}
}
Mühle, Henri; Nadeau, Philippe. A poset structure on the alternating group generated by 3-cycles. Algebraic Combinatorics, Volume 2 (2019) no. 6, pp. 1285-1310. doi : 10.5802/alco.83. https://alco.centre-mersenne.org/item/ALCO_2019__2_6_1285_0/

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