Andrews, George E.George E.AndrewsDixit, AtulAtulDixitYee, Ae JaAe JaYee2025-08-302025-08-302015-12-0110.1007/s40993-015-0020-82-s2.0-85006624407https://d8.irins.org/handle/IITG2025/22638The generating function of partitions with repeated (resp. distinct) parts such that each odd part is less than twice the smallest part is shown to be the third order mock theta function ω(q) (resp. ν(−q)). Similar results for partitions with the corresponding restriction on each even part are also obtained, one of which involves the third order mock theta function ϕ(q). Congruences for the smallest parts partition function(s) associated to such partitions are obtained. Two analogues of the partition-theoretic interpretation of Euler’s pentagonal number theorem are also obtained.trueGenerating functions | Mock theta functions | Partitions | Pentagonal number theorem | Smallest parts functionsArticlehttps://link.springer.com/content/pdf/10.1007%2Fs40993-015-0020-8.pdf236395551 December 20155119arJournal44