Olsson, Jørn B.; Stanton, Dennis Block inclusions and cores of partitions. (English) Zbl 1173.20010 Aequationes Math. 74, No. 1-2, 90-110 (2007). 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. Cited in 5 ReviewsCited in 46 Documents 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 Keywords:blocks of partitions; characters; cores of partitions; symmetric groups; generating functions PDFBibTeX XMLCite \textit{J. B. Olsson} and \textit{D. Stanton}, Aequationes Math. 74, No. 1--2, 90--110 (2007; Zbl 1173.20010) Full Text: DOI