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Abstract

Recently, Nath and Sellers established a characterization of the number of spin characters of $ \hat{S}_n $ and $ \hat{A}_n $ modulo 2 and 3, where $ \hat{S}_n $ and $ \hat{A}_n $ are the double covering groups of the symmetric group $S_n$ and the alternating group $A_n$, respectively. They also obtained infinitely many Ramanujan-like congruences modulo 2 and 3 for the number of spin characters of $ \hat{S}_n $ and $ \hat{A}_n $. Motivated by their work, we study congruences modulo 5 for the number of spin characters of $ \hat{S}_n $ and $ \hat{A}_n $.