The $(s,s+d,\dots ,s+pd)$-core partitions and the rational Motzkin paths

Hyunsoo Cho, JiSun Huh, Jaebum Sohn

In this paper, we propose an $(s+d,d)$-abacus for $(s,s+d,\dots ,s+pd)$-core partitions and establish a bijection between the $(s,s+d,\dots ,s+pd)$-core partitions and the rational M…