The corresponding article has been published in Manuscripta Math. 63 (1989), 129-156.

Christian Krattenthaler

Enumeration of lattice paths and generating functions for skew plane partitions

Abstract. n-dimensional lattice paths not touching the hyperplanes xi-xi+1 = -1, j=1,2,...,n, are counted by four different statistics, one of which is MacMahon's major index. By a reflection-like proof, heavily relying on Zeilberger's (Discrete Math. 44 (1983), 325-326) solution of the n-candidate ballot problem, determinantal expressions are obtained. As corollaries the generating functions for skew plane partitions, column-strict skew plane partitions, reverse skew plane partitions and column-strict reverse skew plane partitions, respectively, are evaluated, thus establishing partly new results, partly new proofs for known theorems in the theory of plane partitions.

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