Tuesday, November 27, 2018 3:30pm to 4:30pm

About this Event

3620 South Vermont Avenue, Los Angeles, CA 90089

**Richard Stanley
Emeritus Professor of Mathematics, MIT**

Abstract:

A parking function of length n is a sequence *a*_1, *a*_2, ... , an of positive integers whose increasing rearrangement *b*_1 \le *b*_2 \le ... \le *b*_*n* satisfies *b*_*i* \le *i*. Parking functions go back to Pyke in 1959; the term "parking function" and the connection with the parking of cars is due to Konheim and Weiss (1966). Pollak gave an elegant proof that the number of parking functions of length *n* is (*n* + 1)^{*n*-1}. There are close connections between parking functions and other combinatorial objects such as trees, noncrossing partitions, and the Shi hyperplane arrangement. Parking functions arise in several unexpected algebraic areas, such as representations of the symmetric group and Haiman's theory of diagonal harmonic. Parking functions also have a number of natural generalizations which fit together in a nice way. We will survey these aspects of the theory of parking functions.

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