1. The World of P and Q: Congruences, Identities and Asymptotics Open Access Author: Chen, Xiaohang Title: The World of P and Q: Congruences, Identities and Asymptotics Graduate Program: Mathematics Keywords: Integer Partitionsq-SeriesCongruencesIdentitiesAsymptoticsPatterns in Inversion SequencesLinked Partition IdealsRogers–Ramanujan Type IdentitiesCircle Method File: Download Shane-Dissertation.pdf Committee Members: George Andrews, Chair & Dissertation AdvisorDonald Richards, Outside Unit & Field MemberAe Ja Yee, Major Field MemberCarina Curto, Program Head/ChairWen-Ching Li, Major Field Member