On the action of the toggle group of the Dynkin diagram of type A

Yasuhide Numata, Yuiko Yamanouchi

Published 2021-03-30Version 1

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.