# Extending the parking space

@article{Berget2013ExtendingTP, title={Extending the parking space}, author={Andrew Berget and Brendon Rhoades}, journal={J. Comb. Theory, Ser. A}, year={2013}, volume={123}, pages={43-56} }

The action of the symmetric group S"n on the set Park"n of parking functions of size n has received a great deal of attention in algebraic combinatorics. We prove that the action of S"n on Park"n extends to an action of S"n"+"1. More precisely, we construct a graded S"n"+"1-module V"n such that the restriction of V"n to S"n is isomorphic to Park"n. We describe the S"n-Frobenius characters of the module V"n in all degrees and describe the S"n"+"1-Frobenius characters of V"n in extreme degrees… CONTINUE READING

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