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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.

title = {Refined counting of core partitions into $d$-distinct parts},