# ALGEBRAIC COMBINATORICS

On the action of the toggle group of the Dynkin diagram of type $A$
Algebraic Combinatorics, Volume 5 (2022) no. 1, pp. 149-161.

In this article, we consider involutions, called togglings, on the set of independent sets of the Dynkin diagram of type $A$, 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.

Accepted:
Revised after acceptance:
Published online:
DOI: 10.5802/alco.204
Classification: 20B20,  05E16,  05C69
Keywords: Coxeter groups; Togglings of independent sets; Fibonacci sequence; Symmetric group; Transitive actions.
Numata, Yasuhide 1; Yamanouchi, Yuiko 2

1 Department of Mathematics Shinshu University Matsumoto Japan
2 Graduate School of Science and Technology Shinshu University Matsumoto Japan
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Numata, Yasuhide; Yamanouchi, Yuiko. On the action of the toggle group of the Dynkin diagram of type $A$. Algebraic Combinatorics, Volume 5 (2022) no. 1, pp. 149-161. doi : 10.5802/alco.204. https://alco.centre-mersenne.org/articles/10.5802/alco.204/

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