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Block inclusions and cores of partitions. (English) Zbl 1173.20010

Summary: 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.

MSC:

20C30 Representations of finite symmetric groups
05A17 Combinatorial aspects of partitions of integers
05E10 Combinatorial aspects of representation theory
20C20 Modular representations and characters
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