Color Partition Identities Arising from Ramanujan’s Theta-Functions

Abstract

We establish several partition identities with distinct colors that arise from Ramanujan's theta-function identities and formulas for multipliers in the theory of modular equations. Also, we deduce few partition congruences as a corollary of some partition identities.

Arithmetic properties of 5-regular bipartitions

“…Proof. In [11] the authors and Sumanth Bharadwaj employ theta function identities of Ramanujan to show that…”

Congruences Modulo 2 for Certain Partition Functions

“…Proof. In [11], we used Ramanujan's theta function identities to derive the identities (−q 3 ; q 6 ) ∞ (−q 5 ; q 10 ) ∞ − (q 3 ; q 6 ) ∞ (q 5 ; q 10 ) ∞ = 2q f 12 f 20…”