#####
Séminaire Lotharingien de Combinatoire, B25b (1990), 4
pp.

[Formerly: Publ. I.R.M.A. Strasbourg, 1991, 462/S-25, p.
113-116.]

# Christian Krattenthaler, S.G. Mohanty

# On Lattice Path Counting by Major and Descents

**Abstract.**
*n*-dimensional lattice paths which do not touch the hyperplanes
*x*(*i*)-*x*(*i*+1)=-1, *i*=1,2,...,(*n*-1)
and *x*(*n*)-*x*(1)=-1-*K* are
enumerated by MacMahon's major index and variations of the major
index. A formula involving determinants is obtained. For *n*=2 we
also present a formula for counting these lattice paths
simultaneously by major and descents.
This paper is a summary of the articles that appeared in:

Europ. J. Combin. 14 (1993), 43-51,

Discrete Math. 126 (1994), 195-208.

The following versions are available: