Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Acta Arithmetica / All issues

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 $\hat{A}_n$.