In his 1984 AMS Memoir, George Andrews introduced the notion of generalized Frobenius partitions or, more simply, F-partitions extending the Frobenius symbol representation of integer partitions using arrays having two rows of equal length. In 2022, Jiang, Rolen, and Woodbury considered (k, a)-colored F-partition functions, \(c\psi _{k,a}(n)\) , which count the Frobenius symbols in a more generalized form allowing unequal lengths of the rows besides other conditions. In this paper, we focus on specific cases of \(c\psi _{k,a}(n)\) , present their generating functions in terms of q-products, and prove a number of congruences satisfied by these functions. Notably, our study uncovers the following Ramanujan-like congruences: \(\begin{aligned} c\psi _{6,2}(5n+4)&\equiv 0 \pmod 5, \\ c\psi _{8,3}(7n+5)&\equiv 0 \pmod 7, \\ c\psi _{12,5}(11n+6)&\equiv 0 \pmod {11}. \end{aligned}\) We use properties of Ramanujan’s theta functions and integer matrix exact covering system to arrive at our results.
