On pairs of lattice paths with a given number of intersections
The author gives another proof for the number of ordered pairs of paths in the integer lattice \(\mathbb{Z}\times\mathbb{Z}\) with a prescribed number of intersection points. This is done by constructing a bijection algorithm between the set of these pairs and some combinatorial set generated by nonintersecting pairs. The first formula for the mentioned number was recently given by \textit{I. M. Gessel} and \textit{W. Shur} [J. Comb. Theory, Ser. A 75, No. 2, 243-253, Art. No. 0075 (1996; Zbl 0866.05002)]. In conclusion some complicated binomial identities are established.
scientific article; zbMATH DE number 1016778