Arithmetic properties of (2, 3)-regular overcubic bipartitions

Abstract

PurposeLet b¯2,3(n), which enumerates the number of (2, 3)-regular overcubic bipartition of n. The purpose of the paper is to describe some congruences modulo 8 for b¯2,3(n). For example, for each α ≥ 0 and n ≥ 1, b¯2,3(8n+5)≡0(mod8), b¯2,3(2⋅3α+3n+4⋅3α+2)≡0(mod8).Design/methodology/approachH.C. Chan has studied the congruence properties of cubic partition function a(n), which is defined by ∑n=0∞a(n)qn=1(q;q)∞(q2;q2)∞.FindingsTo establish several congruence modulo 8 for b¯2,3(n), here the author keeps to the classical spirit of q-series techniques in the proofs.Originality/valueThe results established in the work are extension to those proved in ℓ-regular cubic partition pairs.