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On Lattice Path Counting by Major Index and...
Journal article

On Lattice Path Counting by Major Index and Descents

Abstract

A formula for counting lattice paths in the plane from μ = (μ1, μ2) to λ = (λ1, λ2) which do not cross the lines y = x + d and y = x + c, where c, d ϵ 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 applications, formulas for the joint distribution of Kolmogorov-Smirnov and run statistics are derived.

Authors

Krattenthaler C; Mohanty SG

Journal

European Journal of Combinatorics, Vol. 14, No. 1, pp. 43–51

Publisher

Elsevier

Publication Date

January 1, 1993

DOI

10.1006/eujc.1993.1007

ISSN

0195-6698

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