In this article, we consider involutions, called togglings, on the set of independent sets of the Dynkin diagram of type , or a path graph. We are interested in the action of the subgroup of the symmetric group of the set of independent sets generated by togglings. We show that the subgroup coincides with the symmetric group.
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Mots clés : Coxeter groups; Togglings of independent sets; Fibonacci sequence; Symmetric group; Transitive actions.
@article{ALCO_2022__5_1_149_0, author = {Numata, Yasuhide and Yamanouchi, Yuiko}, title = {On the action of the toggle group of the {Dynkin} diagram of type $A$}, journal = {Algebraic Combinatorics}, pages = {149--161}, publisher = {MathOA foundation}, volume = {5}, number = {1}, year = {2022}, doi = {10.5802/alco.204}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.204/} }
TY - JOUR AU - Numata, Yasuhide AU - Yamanouchi, Yuiko TI - On the action of the toggle group of the Dynkin diagram of type $A$ JO - Algebraic Combinatorics PY - 2022 SP - 149 EP - 161 VL - 5 IS - 1 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.204/ DO - 10.5802/alco.204 LA - en ID - ALCO_2022__5_1_149_0 ER -
%0 Journal Article %A Numata, Yasuhide %A Yamanouchi, Yuiko %T On the action of the toggle group of the Dynkin diagram of type $A$ %J Algebraic Combinatorics %D 2022 %P 149-161 %V 5 %N 1 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/alco.204/ %R 10.5802/alco.204 %G en %F ALCO_2022__5_1_149_0
Numata, Yasuhide; Yamanouchi, Yuiko. On the action of the toggle group of the Dynkin diagram of type $A$. Algebraic Combinatorics, Tome 5 (2022) no. 1, pp. 149-161. doi : 10.5802/alco.204. http://www.numdam.org/articles/10.5802/alco.204/
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