Geodesic
On Lattice Path Counting by Major and Descents
Séminaire lotharingien de combinatoire, Tome 25 (1990)

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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. 

@article{SLC_1990_25_a1,
     author = {Christian Krattenthaler and S.G. Mohanty},
     title = {On {Lattice} {Path} {Counting} by {Major} and {Descents}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {25},
     year = {1990},
     url = {http://geodesic.mathdoc.fr/item/SLC_1990_25_a1/}
}
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Christian Krattenthaler; S.G. Mohanty. On Lattice Path Counting by Major and Descents. Séminaire lotharingien de combinatoire, Tome 25 (1990). http://geodesic.mathdoc.fr/item/SLC_1990_25_a1/