Necessary and sufficient conditions are given for an s-block of integer partitions to be contained in a t-block. The generating function for such partitions is found analytically, and also bijectively, using the notion of an (s, t)-abacus. The largest partition which is both an s-core and a t-core is explicitly given.
Bibliographical noteFunding Information:
The first author was supported by the Danish National Research Council. was supported by NSF grant DMS-0503660.
Copyright 2007 Elsevier B.V., All rights reserved.
- Blocks of partitions