George E. Andrews, Thesis Supervisor Aissa Wade, Thesis Honors Advisor
Keywords:
Rogers-Ramanujan integer partitions distinct parts
Abstract:
Chapter 1: Partitions without sequences of consecutive integers as parts have been studied recently by many authors, including Andrews, Holroyd, Liggett, and Romik, among others. Their results include a description of combinatorial properties, hypergeometric representations for the generating functions, and asymptotic formulas for the enumeration functions. We complete a similar investigation of partitions into distinct parts without sequences, which are of particular interest due to their relationship with the Rogers-Ramanujan identities. Our main results include a double series representation for the generating function, an asymptotic formula for the enumeration function, and several combinatorial inequalities.
Chapter 2: We use the idea of index invariance under the Franklin mapping to prove higher power generalizations of two results discovered by M. V. Subbarao. We then apply similar ideas to a two-variable generalization of the Rogers-Ramanujan identities due to G. E. Andrews.
