The corresponding article has been published in
Manuscripta Math. 69 (1990), 173-202.
Generating functions for plane partitions of a given
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.
For various classes of these (\alpha,\beta)-plane partitions we
compute three different kinds of generating functions. By a combinatorial
method, determinantal expressions are obtained for these generating functions.
In special cases these determinants may be evaluated by a simple determinant
lemma. All known results concerning plane partitions of a given shape are
included. Thus our approach to computation of generating functions for plane
partitions of a given shape provides a uniform method and yields numerous
generalizations of known results.
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