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126 (1994), 195-208,
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Christian Krattenthaler and Sri Gopal Mohanty
q-Generalization of a ballot problem
n-dimensional lattice paths which do not touch the
hyperplanes xi-xi+1=-1, i=1,2, ...
are enumerated by certain statistics, one of which is
MacMahon's major index, the others being variations of it.
By a reflection-like proof,
a formula involving determinants is obtained. It is a q-extension
of Filaseta's (J. Combin. Theory A 39 (1985), 102-111) expression for
the number of elections in a specific ballot problem.
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