A Bijection for Partitions with All Ranks at Least t

Abstract

It follows from the work of Andrews and Bressoud that fort≤1, the number of partitions ofnwith all successive ranks at leasttis equal to the number of partitions ofnwith no part of size 2-t. We give a simple bijection for this identity which generalizes a result of Cheema and Gordon for 2-rowed plane partitions. The bijection yields several refinements of the identity when the partition counts are parametrized by the number of parts and/or the size of the Durfee rectangle. In addition, it gives an interpretation of the difference of (shifted) successive Gaussian polynomials which we relate to other interpretations of Andrews and Fishel. © 1998 Academic Press.