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}.

The following versions are available:

Back to Christian Krattenthaler's home page.