This material has been published in Discrete Math. 126 (1994), 195-208, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Elsevier B.V. This material may not be copied or reposted without explicit permission.

Christian Krattenthaler and Sri Gopal Mohanty

q-Generalization of a ballot problem

Abstract. n-dimensional lattice paths which do not touch the hyperplanes xi-xi+1=-1, i=1,2, ... ,n-1, and xn-x1=-1-K are enumerated by certain statistics, one of which is MacMahon's major index, the others being variations of it. By a reflection-like proof, a formula involving determinants is obtained. It is a q-extension of Filaseta's (J. Combin. Theory A 39 (1985), 102-111) expression for the number of elections in a specific ballot problem.

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