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Generating functions for plane partitions of a given shape

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Abstract

For fixed integers α and β, planar arrays of integers of a given shape, in which the entries decrease at least by α along rows and at least by β along columns, are considered. For various classes of these (α,β)-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 of a given shape provides a uniform proof method and yields numerous generalizations of known results.

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  1. Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090, Vienna, Austria

    Christian Krattenthaler

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  1. Christian Krattenthaler
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Krattenthaler, C. Generating functions for plane partitions of a given shape. Manuscripta Math 69, 173–201 (1990). https://doi.org/10.1007/BF02567918

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  • DOI: https://doi.org/10.1007/BF02567918

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