This material has been published in Europ. J. Combin. 14 (1993), 43-51, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Elsevier B.V. This material may not be copied or reposted without explicit permission.

Christian Krattenthaler and Sri Gopal Mohanty

On lattice path counting by major and descents

Abstract. A formula for counting lattice paths in the plane from \mu =(\mu1,\mu2) to \lambda =(\lambda1,\lambda2) which do not cross the lines y=x+d and y=x+c, where c,d\in Z and d>c, by descents and major index is given. The proof, which is purely combinatorial, uses a bijection on certain two-rowed tableaux. As application, formulas for the joint distribution of Kolmogorov-Smirnov and run statistics are derived.

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