Trimming the permutahedron to extend the parking space
Abstract
Berget and Rhoades asked whether the permutation representation obtained by the action of Sn-1 on parking functions of length n-1 can be extended to a permutation action of Sn. We answer this question in the affirmative. We realize our module in two different ways. The first description involves binary Lyndon words and the second involves the action of the symmetric group on the lattice points of the trimmed standard permutahedron.
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