Hannah E. Burson, Simone Sisneros-Thiry, Armin Straub — Electronic Journal of Combinatorics — Volume 28, Number 1, 2021, Pages 1-21, #P1.37
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.Download
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BibTeX
@article{corepartitions-parts-2021,
author = {Hannah E. Burson and Simone Sisneros-Thiry and Armin Straub},
title = {Refined counting of core partitions into $d$-distinct parts},
journal = {Electronic Journal of Combinatorics},
year = {2021},
volume = {28},
number = {1},
pages = {1--21, #P1.37},
doi = {10.37236/9665},
}