On Lattice Path Counting by Major and Descents
نویسندگان
چکیده
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 ∈ 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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