Abstract
In this paper, we propose an (s+d,d)-abacus for (s,s+d,…,s+pd)-core partitions and establish a bijection between the (s,s+d,…,s+pd)-core partitions and the rational Motzkin paths of type (s+d,−d). This result not only gives a lattice path interpretation of the (s,s+d,…,s+pd)-core partitions but also counts them with an explicit formula. Also we enumerate (s,s+1,…,s+p)-core partitions with k corners and self-conjugate (s,s+1,…,s+p)-core partitions.
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