##### The corresponding article has been published in
Manuscripta Math. **69** (1990), 173-202.

## Christian Krattenthaler

# Generating functions for plane partitions of a given
shape

**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.
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.

The following versions are available:

Back to Christian Krattenthaler's
home page.