On self-conjugate (,  + 1, ...,  + )-core partitions.

Simultaneous core partitions have been widely studied since Anderson's work on the enumeration of (s,t)-core partitions. Amdeberhan and Leven showed that the number of (s,s+1,…,s+k)-core partitions is equal to the number of (s,k)-Dyck paths. In this paper, we prove that self-conjugate (s,s+1,…,s+k)-core partitions are equinumerous with symmetric (s,k)-Dyck paths, confirming a conjecture posed by Cho, Huh and Sohn.