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A solution to the tennis ball problem

2003/11/14 by Anna de Mier, de Mier, Anna, Marc Noy +1
Computer Science · Mathematics · Physics and Astronomy · #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #math.CO #msc:05A15

paper · pdf · doi:10.48550/arxiv.math/0311242

9 pages, Latex

arxiv created 2003/11/14 · openalex publication_date 2003/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a complete solution to the so-called tennis ball problem, which is equivalent to counting lattice paths in the plane that use North and East steps and lie between certain boundaries. The solution takes the form of explicit expressions for the corresponding generating functions. Our method is based on the properties of Tutte polynomials of matroids associated to lattice paths. We also show how the same method provides a solution to a wide generalization of the problem.

Citations

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