James Sellers

Affiliation: Pennsylvania State University

Email: sellersj@psu.edu

Title Of Talk: Infinitely Many Congruences Modulo 5 for 4-Colored Frobenius Partitions

Abstract: In his 1984 AMS Memoir, G. E. Andrews introduced the family of functions $c\phi_k(n)$, which denotes the number of generalized Frobenius partitions of $n$ into $k$ colors. Recently, Baruah and Sarmah, Lin, Sellers, and Xia established several Ramanujan-like congruences for $c\phi_4(n)$ relative to different moduli. In this paper, which is joint work with Michael D. Hirschhorn (UNSW), we employ classical results in $q$-series, the well-known theta functions of Ramanujan, and elementary generating function manipulations to prove a characterization of $c\phi_4(10n+1)$ modulo 5 which leads to an infinite set of Ramanujan-like congruences modulo 5 satisfied by $c\phi_4$. This work greatly extends the recent work of Xia on $c\phi_4$ modulo 5.

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