Sign-patterns of Certain Infinite Products

The signs of Fourier coefficients of certain eta quotients are determined by dissecting expansions for theta functions and by applying a general dissection formula for certain classes of quintuple products. A characterization is given for the coefficient sign patterns for \[ {(q^i;q^i)∞}{(q^p;q^p)∞} \] for integers \( i > 1 \) and primes \( p > 3 \). The sign analysis for this quotient addresses and extends a conjecture of Bringmann et al. for the coefficients of \( (q^2;q^2)∞(q^5;q^5)∞⁻¹ \). The sign distribution for additional classes of eta quotients is considered. This addresses multiple conjectures posed by Bringmann et al.