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Refined counting of core partitions into d-distinct parts

Refined counting of core partitions into d-distinct parts
Hannah E. Burson, Simone Sisneros-Thiry, Armin Straub — Preprint — 2019

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.

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BibTeX

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