The Ramanujan Journal

, Volume 27, Issue 2, pp 229-233

First online:

On core and bar-core partitions

  • Jean-Baptiste GramainAffiliated withInstitut de Mathématiques de Jussieu, Université Denis Diderot, Paris VII, UFR de Mathématiques Email author 
  • , Rishi NathAffiliated withDepartment of Mathematics and Computer Science, York College, City University of New York

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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.


Partitions Bar partitions Core Bar-core

Mathematics Subject Classification (2000)

20C30 20C15 20C20