Catalan Traffic and Integrals on the Grassmannians of Lines

We prove that certain numbers occurring in a problem of paths enumeration, studied by Niederhausen (Catlan Traffic at the Beach, The Electronic Journal of Combinatorics, 9, (2002), 1--17), are top intersection numbers in the cohomology ring of the grassmannians of the lines in the complex projective (n+1)-space.Comment: Excerpt from my Ph.D. Thesis; to appear on "Discrete Mathematics