Identities and Generating Functions for Certain Classes of \(F\)- Partitions

Four generalized theorems involving partitions and \((n+1)\)-color partitions are proved combinatorially. Each of these theorems gives us infinitely many partition identities. We obtain new generating functions for \(F\)-partitions and discuss some particular cases which provide elegant Rogers-Ramanujan type identities for \(F\)-partitions.