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### Parking Spaces

**Algebra & Discrete Mathematics**

Speaker: | Brendon Rhoades, University of Southern California |

Location: | 2112 MSB |

Start time: | Tue, May 22 2012, 2:10PM |

A sequence (a_{1}, ..., a_{n}) of positive integers is aparking functionif its nondecreasing rearrangement (b_{1}, ..., b_{n}) satisfies b_{i}<i+1 for alli. Parking functions were introduced by Konheim and Weiss to study a hashing problem in computer science, but have since received a great deal of attention in algebraic combinatorics. We will define two new objects attached to any (finite, real) reflection group which generalize parking functions and deserve to be called parking spaces. We present a conjecture (proved in some special cases) which asserts a deep relationship between these constructions. This is joint work with Drew Armstrong at the University of Miami and Vic Reiner at the University of Minnesota.