Construction of series as generating functions and verification type proofs for rogers-ramanujan generalization for partitions and overpartitions

Warning The system is temporarily closed to updates for reporting purpose.

Zadeh Dabbagh, Mohammad (2022) Construction of series as generating functions and verification type proofs for rogers-ramanujan generalization for partitions and overpartitions. [Thesis]

[thumbnail of 10487730.pdf] PDF
10487730.pdf

Download (325kB)

Abstract

During the last century, researchers studied integer partition theory extensively. We are more interested in exploring partition identities among many aspects of integer partitions. In this thesis, we study a constructive method developed by Kur sungoz to nd new identities on Rogers-Ramanujan type integer partitions and overpartitions. For this aim, we give a reproof of two Rogers-Ramanujan identities using the constructive method. Combining two types of partitions, we introduced 2-colored Rogers-Ramanujan partitions. By nding some functional equations and using the constructive method, some identities have been found. Our results coincide with some extreme cases of Rogers-Ramanujan-Gordon's identities. A correspondence between colored partitions and those overpartitions is provided. Our second result is nding the missing cases of parity consideration on Rogers- Ramanujan-Gordon's identities due to Andrews's suggestion in his seminal paper about parity in partition identities. Four cases had proven by Sang, Shi, and Yee, we reproved them using the said constructive method and then found and proved the remaining cases by the same method.
Item Type: Thesis
Uncontrolled Keywords: Integer Partitions. -- Partition Identities. -- Overpartitions. -- Colored Partitions. -- q-series. -- Rogers-Ramanujan Type Partitions.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Dila Günay
Date Deposited: 27 Apr 2023 14:10
Last Modified: 27 Apr 2023 14:10
URI: https://research.sabanciuniv.edu/id/eprint/47188

Actions (login required)

View Item
View Item