A solution to the tennis ball problem
We present a complete solution to the so-called tennis ball problem, which is equivalent to counting the number of 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 proper-ties 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. (c) 2005 Elsevier B.V. All rights reserved.
lattice path tutte polynomial kernel method