New classes of Infinite \(3\)-way Partition Identity

We study four \(q\)-series. Each of which is interpreted combinatorially in three different ways. This results in four new classes of infinite \(3\)-way partition identities. In some particular cases we get even \(4\)-way partition identities. Our every \(3\)-way identity gives us three Roderick-Ramanujan type identities and \(4\)-way identity gives six. Several partition identities due to Gordon \((1965)\), Hirschhorn \((1979)\), Subbarao \((1985)\), Blecksmith et al. \((1985)\), Agarwal \((1988)\) and Subbarao and Agarwal (1988) are obtained as particular cases of our general theorems.