Home > A Variation on the Tennis Ball Problem

A Variation on the Tennis Ball Problem

When
Start: 03/25/2008 - 11:15am
End  : 03/25/2008 - 12:10pm

Category
Algebra/Number Theory/Combinatorics Seminar

Speaker
Naiomi Cameron (Lewis and Clark College)

Abstract

We consider a variation on the Tennis Ball Problem studied by Mallows-Shapiro and Merlini, et al. The $ s $-Tennis Ball problem is the following: At first turn, you are given $ s $ balls labeled $ 1,2,\dots,s $, where $ s $ is a fixed positive integer. You toss one of them out of the window onto the lawn. At the second turn, balls numbered $ s+1,s+2,\ldots,2s $ are given to you and now you toss any of the $ 2s-1 $ remaining balls onto the lawn. This continues for $ n $ turns. We consider two questions. First, how many different combinations of balls on the lawn are possible after $ n $ turns? Second, what is the sum of the labels of the balls on the lawn, over all distinct possibilities, after $ n $ turns? In the case where $ s=2, $ the solution to the original problem is the well known Catalan numbers. The variations discussed in this talk yield the Motzkin numbers and other related sequences.

Where
Millikan 208, Pomona College

Misc. Information

We provide catered lunch for all the participants, served before the seminar. So feel free to bring your hungry-for-food tummies as well as your thirsty-for-math minds!