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

Abstract 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.

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