Refined counting of core partitions into $d$-distinct parts

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

Refined counting of core partitions into $d$-distinct parts

Combinatorics 2019-10-15 v1 Number Theory

Authors: Hannah E. Burson , Simone Sisneros-Thiry , Armin Straub

Abstract

Using a combinatorial bijection with certain abaci diagrams, Nath and Sellers have enumerated $(s, m s \pm 1)$ -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 $(s, m s \pm r)$ -core partitions. As an application of our approach, we obtain the average and maximum number of parts of these core partitions.

Keywords

core partitions d-distinct parts abaci diagrams combinatorial bijection enumeration average number of parts

Cite

@article{arxiv.1910.05423,
  title  = {Refined counting of core partitions into $d$-distinct parts},
  author = {Hannah E. Burson and Simone Sisneros-Thiry and Armin Straub},
  journal= {arXiv preprint arXiv:1910.05423},
  year   = {2019}
}

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18 pages

Refined counting of core partitions into $d$-distinct parts

Abstract

Keywords

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