##### 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
*x*_{i}-x_{i+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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