Title
Some Variations on the Tennis Ball Problem
Document Type
Article
Publication Date
2004
Abstract
Our study looks at Catalan, Motzkin, and Schr?der numbers. Catalan numbers are very well known mathematically and extensive research has been done highlighting their interesting properties. In contrast, Motzkin and Schroder numbers are not so well developed. We have been able to adapt certain techniques to different sequences. We have looked at variations of the Tennis Ball problem that generate Catalan and Motzkin numbers. We also investigated a recursive formula for counting Motzkin paths with flaws in terms of Motzkin numbers and came up with a combinatorial proof of Motzkin paths with 2 and 3 flaws in terms of normal Motzkin paths. Path and binary tree interpretations have also been looked at, leading to interesting results.
Recommended Citation
Biller, Nicholas, "Some Variations on the Tennis Ball Problem" (2004). URC Student Scholarship.
http://scholar.oxy.edu/urc_student/880
Advisor
N. Cameron
Department
math
Support
Howard Hughes Medical Institute Grant Fellowship
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