We investigate the poset structure on the alternating group that arises when the latter is generated by -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. -cycles, and we compare our results to this case along the way. In particular, noncrossing partitions arise naturally in both settings.
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DOI : 10.5802/alco.83
Mots clés : 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},
pages = {1285--1310},
publisher = {MathOA foundation},
volume = {2},
number = {6},
year = {2019},
doi = {10.5802/alco.83},
mrnumber = {4049847},
language = {en},
url = {http://www.numdam.org/articles/10.5802/alco.83/}
}
TY - JOUR AU - Mühle, Henri AU - Nadeau, Philippe TI - A poset structure on the alternating group generated by 3-cycles JO - Algebraic Combinatorics PY - 2019 SP - 1285 EP - 1310 VL - 2 IS - 6 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.83/ DO - 10.5802/alco.83 LA - en ID - ALCO_2019__2_6_1285_0 ER -
%0 Journal Article %A Mühle, Henri %A Nadeau, Philippe %T A poset structure on the alternating group generated by 3-cycles %J Algebraic Combinatorics %D 2019 %P 1285-1310 %V 2 %N 6 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/alco.83/ %R 10.5802/alco.83 %G en %F ALCO_2019__2_6_1285_0
Mühle, Henri; Nadeau, Philippe. A poset structure on the alternating group generated by 3-cycles. Algebraic Combinatorics, Tome 2 (2019) no. 6, pp. 1285-1310. doi : 10.5802/alco.83. http://www.numdam.org/articles/10.5802/alco.83/
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