##### The corresponding article has been published in
Sitz.ber. d. ÖAW Math.-naturwiss. Klasse **198** (1989), 87-107.

## Christian Krattenthaler

# Counting lattice paths with a linear boundary I

**Abstract.**
Lattice paths in the plane that do not touch a given line are counted
with respect to four different statistics, which were introduced by
J. Fürlinger and J. Hofbauer (J. Combin. Theory Ser. A **40** (1985),
248-264) and generalize the well-known descent-major statistics. We give
generating functions, recurrence relations, and convolution identities
for the resulting numbers, which are generalizations of the well-known
Gould numbers *A*_{ n}(*a,b*) = *a/*(*a+bn*)
*\binom* {*a+bn*} {*n*}.
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