Mathematics Colloquium by Brian Kamau '23

Wed, March 15th, 2023
1:00 pm - 1:45 pm

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On the Outcome map of MVP Parking Functions: Permutations Avoiding 321 and 3412, and Motzkin Paths by Brian Kamau ’23, Mathematics Colloquium, Wednesday, March 15, 1 – 1:45 pm, North Science Building 113, Wachenheim.

Abstract:  I will be introducing a new parking procedure called MVP parking in which n cars sequentially enter a one-way street with a preferred parking spot from the n parking spots on the street.  If their preferred spot is empty, they park there.  If all cars can park under this parking procedure, we say the list of preferences of the n cars is an MVP parking function of length n.  We show that the set of (classical) parking functions is exactly the set of MVP parking functions although the parking outcome (order in which the cars park) is different under each parking process. 

I will also be describing the outcome of the MVP parking process, what is the number of MVP parking functions resulting in that given outcome?  The main result establishes a bound for this count which is tight precisely when the permutation describing the parking outcome avoids certain patterns.  Finally, I show that the number of MVP parking functions that park in reverse order is given by the nth Motzkin number.

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