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Trimming the permutahedron to extend the parking space

Trimming the permutahedron to extend the parking space

Berget and Rhoades asked whether the permutation representation obtained by the action of S n-1 on parking functions of length n-1 can be extended to a permutation action of S n . We answer this question in the affirmative. We realize our module in two different ways. The first description …