This material has been published in
Europ. J. Combin.
14 (1993), 43-51,
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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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