Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415532 | Journal of Number Theory | 2015 | 9 Pages |
In his 1984 AMS Memoir, Andrews introduced the k-colored generalized Frobenius partition function cÏk(n), which denotes the number of generalized Frobenius partitions of n with k colors. Recently, Baruah and Sarmah found the generating function for cÏ6(n). They also established 2- and 3-dissections of the generating function for cÏ6(n) and proved that cÏ6(2n+1)â¡0(mod4), cÏ6(3n+1)â¡cÏ6(3n+2)â¡0(mod9). Furthermore, they conjectured that cÏ6(3n+2)â¡0(mod27) for nâ¥0. In this paper, we confirm this conjecture by employing the generating function for cÏ6(3n+2) given by Baruah and Sarmah and the (p,k)-parametrization of theta functions due to Alaca, Alaca and Williams. Moreover, we conjecture that for nâ¥0, cÏ6(9n+7)â¡0(mod27) and cÏ6(27n+16)â¡0(mod35).