Studies of partition functions with conditions on parts and parity
Open Access
Author:
Passary, Donny
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
September 27, 2019
Committee Members:
George E Andrews, Dissertation Advisor/Co-Advisor George E Andrews, Committee Chair/Co-Chair Ae Ja Yee, Committee Chair/Co-Chair Wen-Ching Winnie Li, Committee Member Donald Richards, Outside Member James A Sellers, Committee Member Alexei Novikov, Program Head/Chair Ae Ja Yee, Dissertation Advisor/Co-Advisor
This dissertation explores four topics in partition theory, with main themes on parts and parities conditions. The first topic studies many properties of the EO-partitions by Andrews, especially the results analogous to the work of Atkin and Swinnerton-Dyer. The second topic deals with the concept of Andrews' separable integer partition classes, which yields alternate proofs for many partition identities including little Gollnitz identities. The third topic gives infinite families of congruences for partition functions arising from Ramanujan's mock theta functions. Some other related identities analogue to Euler's pentagonal number theorem are also proved. Finally, the fourth topic presents a combinatorial proof for an overpartition identity, derived from the truncated version of a certain theta series identity.
