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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A determinant evaluation and some enumeration results for plane
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 ai and bi,
respectively, can be given by a determinant. We give a new
evaluation of this determinant for some special choices of the row
bounds ai and bi.
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