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.

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