Krattenthaler, Christian; Mohanty, S. G. On lattice path counting by major and descents. (English) Zbl 0981.05510 Sémin. Lothar. Comb. 25, B25b, 4 p. (1990). Summary: \(n\)-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: Eur. J. Comb. 14, 43-51 (1993; Zbl 0777.05008), Discrete Math. 126, 195-208 (1994; Zbl 0790.60014). MSC: 05A15 Exact enumeration problems, generating functions 60C05 Combinatorial probability 62E15 Exact distribution theory in statistics Citations:Zbl 0777.05008; Zbl 0790.60014 PDFBibTeX XMLCite \textit{C. Krattenthaler} and \textit{S. G. Mohanty}, Sémin. Lothar. Comb. 25, B25b, 4 p. (1990; Zbl 0981.05510) Full Text: EuDML EMIS