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Congruences modulo 5 for the number of spin characters of the double covers of the symmetric and alternating groups

Volume 187 / 2019

Ernest X. W. Xia 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 $.

Authors

  • Ernest X. W. XiaDepartment of Mathematics
    Jiangsu University
    Zhenjiang, Jiangsu 212013, P.R. China
    e-mail

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