On core and bar-core partitions
- First Online:
- Cite this article as:
- Gramain, J. & Nath, R. Ramanujan J (2012) 27: 229. doi:10.1007/s11139-011-9309-y
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.