Proof of a Limited Version of Mao's Partition Rank Inequality using a Theta Function Identity

Rupam Barman, Archit Pal Singh Sachdeva

Ramanujan's congruence $p(5k+4)\equiv 0(\mathrm{mod}5)$ led Dyson \cite{dyson} to conjecture the existence of a measure "rank" such that $p(5k+4)$ partitions of $5k+4$ could be divided i…