Geodesic
The Alternating Group Generated by 3-Cycles
Séminaire lotharingien de combinatoire, 78B (2017)

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We investigate the partial order on the alternating group generated by all 3-cycles. We first describe the cover relations in this poset. Permutations with odd cycles occur naturally, and we study the lower intervals they induce. These intervals are naturally embedded in the lattices of noncrossing partitions, and we provide several enumeration formulas for them. We also study the natural action of the braid group on the maximal chains in any given interval, and determine when this action is transitive. We also outline the many ways in which our construction can, or could, be extended. 

@article{SLC_2017_78B_a35,
     author = {Henri M\"uhle and Philippe Nadeau},
     title = {The {Alternating} {Group} {Generated} by {3-Cycles}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a35/}
}
TY  - JOUR
AU  - Henri Mühle
AU  - Philippe Nadeau
TI  - The Alternating Group Generated by 3-Cycles
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a35/
ID  - SLC_2017_78B_a35
ER  - 
%0 Journal Article
%A Henri Mühle
%A Philippe Nadeau
%T The Alternating Group Generated by 3-Cycles
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a35/
%F SLC_2017_78B_a35
Henri Mühle; Philippe Nadeau. The Alternating Group Generated by 3-Cycles. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a35/