Geodesic
Generator Sets for the Alternating Group
Séminaire lotharingien de combinatoire, Tome 65 (2011-2012)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

Although the alternating group is an index 2 subgroup of the symmetric group, there is no generating set that gives a Coxeter structure on it. Various generating sets were suggested and studied by Bourbaki, Mitsuhashi, Regev and Roichman, Vershik and Vserminov, and others. In a recent work of Brenti, Reiner and Roichman, it is explained that palindromes in Mitsuhashi's generating set play a role similar to that of reflections in a Coxeter system.

We study in detail the length function with respect to the set of palindromes. Results include an explicit combinatorial description, a generating function, and an interesting connection to Broder's restricted Stirling numbers. 

@article{SLC_2011-2012_65_a1,
     author = {Aviv Rotbart},
     title = {Generator {Sets} for the {Alternating} {Group}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {65},
     year = {2011-2012},
     url = {http://geodesic.mathdoc.fr/item/SLC_2011-2012_65_a1/}
}
TY  - JOUR
AU  - Aviv Rotbart
TI  - Generator Sets for the Alternating Group
JO  - Séminaire lotharingien de combinatoire
PY  - 2011-2012
VL  - 65
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2011-2012_65_a1/
ID  - SLC_2011-2012_65_a1
ER  - 
%0 Journal Article
%A Aviv Rotbart
%T Generator Sets for the Alternating Group
%J Séminaire lotharingien de combinatoire
%D 2011-2012
%V 65
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2011-2012_65_a1/
%F SLC_2011-2012_65_a1
Aviv Rotbart. Generator Sets for the Alternating Group. Séminaire lotharingien de combinatoire, Tome 65 (2011-2012). http://geodesic.mathdoc.fr/item/SLC_2011-2012_65_a1/