Certain Identities Associated With Character Formulas, Continued Fraction and Combinatorial Partition Identities

Abstract

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.

A Family of Theta-Function Identities Based upon Combinatorial Partition Identities Related to Jacobi’s Triple-Product Identity

“…Thirdly, we prove the third relationship (31) of Theorem 3. For this purpose, we first apply the identity ( 9) (with q replaced by q 3 , q 7 and q 21 ) under the given precondition of (25), and then use (20) and (21). We thus find for the values of P and Q that…”

“…Ever since the year 2015, several new advancements and generalizations of the existing results were made in regard to combinatorial partition-theoretic identities (see, for example, [8,[15][16][17][18][19][20][21][22][23][24]). In particular, Chaudhary et al generalized several known results on character formulas (see [22]), Roger-Ramanujan type identities (see [19]), Eisenstein series, the Ramanujan-Göllnitz-Gordon continued fraction (see [20]), the 3-dissection property (see [18]), Ramanujan's modular equations of degrees 3, 7, and 9 (see [16,17]), and so on, by using combinatorial partition-theoretic identities.…”

Note on Some Character Formulas

“…Here we recall certain interesting interrelations among character formulas, combinatorial partition identities and continued partition identities (see [7,Section 3]). 2, 1, 1, 1, 2).…”

“…Certain interesting special cases of (16) are recalled (see [1, p. 106, Theorem 3]; see also [3]- [7] and [9] ):…”

“…Chaudhary and Choi [7] presented 14 identities which reveal certain interesting interrelations among character formulas, combinatorial partition identities and continued partition identities. In this sequel, we aim to give slightly modified versions for 8 identities which are chosen among the above-mentioned 14 formulas.…”