On core and bar-core partitions
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- Gramain, J. & Nath, R. Ramanujan J (2012) 27: 229. doi:10.1007/s11139-011-9309-y
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If s and t are relatively prime integers, J.B. Olsson proved in (J. Comb. Theory, Ser. A 116:733–740, 2009) that the s-core of a t-core partition is again a t-core partition, and that the s-bar-core of a t-bar-core partition is again a t-bar-core partition. Here generalised results are proved for partitions and bar partitions when the restriction that s and t be relatively prime is removed.