A BIJECTION FOR PARTITIONS WITH ALL RANKS AT LEAST T

It follows from the work of Andrews and Bressoud that for t less than or equal to 1, the number of partitions of n with all successive ranks at least t is equal to the number of partitions of n with no part of size 2 - t. We give a simple bijection for this identity which general izes a result of Cheema and Gordon for 2 rowed plane partitions. The b ijection 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 diff erence of(shifted) successive Gaussian polynomials which we relate to other interpretations of Andrews and Fishel. (C) 1998 Academic Press.