New Enumerations for l-Regular Bipartitions Under Modulo 2 and 3

For any positive integer l, Bln represents the number of l-regular bipartitions. By employing q-identities, modular equations, and Rogers–Ramanujan continued fraction identities, we establish new congruences under modulo 2 and 3. Our analysis is fundamentally based on the continued fraction and a collection of associated q-series identities. In particular, we exploit the modular and transformation properties of the well-known continued fraction, together with its deep connections to Rogers–Ramanujan continued fraction type identities, to derive explicit generating function dissections and establish the desired congruence relations.