ALGEBRAIC COMBINATORICS

no. 6
A poset structure on the alternating group generated by 3-cycles
Mühle, Henri1; Nadeau, Philippe2
1 Technische Universität Dresden Institut für Algebra Zellescher Weg 12–14 01069 Dresden Germany.
2 Univ. Lyon CNRS Université Claude Bernard Lyon 1 UMR5208 Institut Camille Jordan F-69622 Villeurbanne France.
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.

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Accepted:
Published online:
DOI: 10.5802/alco.83
Classification: 06A07, 05A10, 05E15, 20B35
Keywords: Symmetric group, Alternating group, Noncrossing partitions, Hurwitz action, zeta polynomial
Mühle, Henri 1; Nadeau, Philippe 2

1 Technische Universität Dresden Institut für Algebra Zellescher Weg 12–14 01069 Dresden Germany.
2 Univ. Lyon CNRS Université Claude Bernard Lyon 1 UMR5208 Institut Camille Jordan F-69622 Villeurbanne France.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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/articles/10.5802/alco.83/

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