Infinitely many congruences modulo 5 for 4-colored Frobenius partitions

In his 1984 AMS Memoir, Andrews introduced the family of functions (Formula presented.) which denotes the number of generalized Frobenius partitions of (Formula presented.) into (Formula presented.) colors. Recently, Baruah and Sarmah, Lin, Sellers, and Xia established several Ramanujan-like congruences for (Formula presented.) relative to different moduli. In this paper, employing classical results in (Formula presented.) -series, the well-known theta functions of Ramanujan, and elementary generating function manipulations, we prove a characterization of (Formula presented.) modulo 5 which leads to an infinite set of Ramanujan-like congruences modulo 5 satisfied by (Formula presented.) This work greatly extends the recent work of Xia on (Formula presented.) modulo 5.