The Ramanujan Journal

, Volume 27, Issue 2, pp 229–233 | Cite as

On core and bar-core partitions

  • Jean-Baptiste Gramain
  • Rishi Nath


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.


Partitions Bar partitions Core Bar-core 

Mathematics Subject Classification (2000)

20C30 20C15 20C20 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institut de Mathématiques de JussieuUniversité Denis Diderot, Paris VII, UFR de MathématiquesParis Cedex 05France
  2. 2.Department of Mathematics and Computer Science, York CollegeCity University of New YorkJamaicaUSA

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