# 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 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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