The Ramanujan Journal

, Volume 27, Issue 2, pp 229–233

On core and bar-core partitions


    • Institut de Mathématiques de JussieuUniversité Denis Diderot, Paris VII, UFR de Mathématiques
  • Rishi Nath
    • Department of Mathematics and Computer Science, York CollegeCity University of New York

DOI: 10.1007/s11139-011-9309-y

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.


Partitions Bar partitions Core Bar-core

Mathematics Subject Classification (2000)

20C30 20C15 20C20

Copyright information

© Springer Science+Business Media, LLC 2011