Results on bar-core partitions, core shifted Young diagrams, and doubled distinct cores

Abstract

Self-conjugate core partitions, bar-core partitions, core shifted Young diagrams (or CSYDs), and doubled distinct core partitions have been studied independently. In this paper, we show that doubled distinct cores and CSYDs are special cases of bar-core partitions. From this fact together with the abacus construction, we find path interpretations of bar-cores, CSYDs, and doubled distinct cores on (s,t)-cores and (s,s+d,s+2d)-cores, respectively. As a result, we get the number of these core partitions. © 2023 Elsevier B.V.