On self-conjugate (

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.