Abstract. Folsom [10] investigated character formulas and Chaudhary [7] expressed those formulas in terms of continued fraction identities. Andrews et al.[2] introduced and investigated combinatorial partition identities. By using and combining known formulas, we aim to present certain interrelationships among character formulas, combinatorial partition identities and continued partition identities.

We aim to express the results involving Ramanujan's modular equation of degree seven in [10] in terms of combinatorial partition identities.

In recent work, Folsom discussed character formulas for classical mock theta functions of Ramanujan. Here, we suggest representations for character formulas in terms of continued fraction identities or in more precise language, we can say an applications of continued fraction identities to character formulas. As a consequence, we obtain fourteen new results.

Abstract. Adiga and Anitha [1] investigated the Ramanujan's continued fraction (18) to present many interesting identities. Motivated by this work, by using known formulas, we also investigate the Ramanujan's continued fraction (18) to give certain relationships between the Ramanujan's continued fraction and the combinatorial partition identities given by Andrews et al. [3].

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