Congruences modulo 5 for the number of spin characters of the double covers of the symmetric and alternating groups
Volume 187 / 2019
Acta Arithmetica 187 (2019), 255-269
MSC: Primary 11P83; Secondary 05A17.
DOI: 10.4064/aa170920-12-4
Published online: 17 December 2018
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 $.
