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On core and bar-core partitions

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Abstract

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.

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Authors and Affiliations

  1. Institut de Mathématiques de Jussieu, Université Denis Diderot, Paris VII, UFR de Mathématiques, 2 place Jussieu, 75251, Paris Cedex 05, France

    Jean-Baptiste Gramain

  2. Department of Mathematics and Computer Science, York College, City University of New York, 94-20 Guy R. Brewer Blvd, Jamaica, NY, 11418, USA

    Rishi Nath

Authors
  1. Jean-Baptiste Gramain
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  2. Rishi Nath
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Correspondence to Jean-Baptiste Gramain.

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Gramain, JB., Nath, R. On core and bar-core partitions. Ramanujan J 27, 229–233 (2012). https://doi.org/10.1007/s11139-011-9309-y

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  • DOI: https://doi.org/10.1007/s11139-011-9309-y

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