2024/04/24 by Keith, William J., Zanello, Fabrizio
#11F33 #11P82 #11P84 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT) #Primary: 11P83 #Secondary: 05A17
paper · doi:10.48550/arxiv.2404.15716
We continue a series of papers studying the parity of families of eta-quotients, which provide implications for the parity of the partition function as well as an overarching conjecture on related q-series. The present article focuses on two classes. One consists of eta-quotients of the form ft3/f1, a distinguished case of Andrews' singular overpartitions that has recently attracted attention among researchers. In addition, we investigate the parity of certain pure eta-powers f1t, appending new results to known density theorems.