##### This material has been published in
"Number-Theoretic Analysis", E. Hlawka,
R. F. Tichy, eds.,
Lect. Notes in Math. 1452, Springer-Verlag, Berlin, New
York, 1990, pp. 121-131,
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## Christian Krattenthaler

# A determinant evaluation and some enumeration results for plane
partitions

### (11 pages)

**Abstract.**
For fixed integers *\alpha* and *\beta*, planar arrays of integers of
a given shape, in which the entries decrease at least by *\alpha* along
rows and at least by *\beta* along columns, are considered. The number of
these (*\alpha,\beta*)-plane partitions in which the first part and the last
part in the *i*'th row are bounded by some integers *a*_{i} and *b*_{i},
respectively, can be given by a determinant. We give a new
evaluation of this determinant for some special choices of the row
bounds *a*_{i} and *b*_{i}.

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