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On the action of the toggle group of the Dynkin diagram of type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math>
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 …