Refined Counting of Core Partitions into $d$-Distinct Parts

  • Hannah E. Burson
  • Simone Sisneros-Thiry
  • Armin Straub


Using a combinatorial bijection with certain abaci diagrams, Nath and Sellers have enumerated $(s,ms\pm 1)$-core partitions into distinct parts. We generalize their result in several directions by including the number of parts of these partitions, by considering $d$-distinct partitions, and by allowing more general $(s,ms\pm r)$-core partitions. As an application of our approach, we obtain the average and maximum number of parts of these core partitions.

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