Core Partitions With d-Distinct Parts

Abstract

In this paper, we study $(s,s+1)$-core partitions with $d$-distinct parts. We obtain results on the number and the largest size of such partitions, so we extend Xiong's paper in which the results are obtained about $(s,s+1)$-core partitions with distinct parts. Also, we propose a conjecture about $(s,s+r)$-core partitions with $d$-distinct parts for $1\le r\le d$.

9 pages

References in corpus (4)

• Theorems, Problems and Conjectures
• Core partitions with distinct parts
• The number of simultaneous core partitions
• On the largest size of $(t,t+1,...,t+p)$-core partitions