Arithmetic of partition functions and q-combinatorics

Integer partitions play important roles in diverse areas of mathematics such as q-series, the theory of modular forms, representation theory, symmetric functions and mathematical physics. Among these, we study the arithmetic of partition functions and q-combinatorics via bijective methods, q-series and modular forms. In particular, regarding arithmetic properties of partition functions, we examine partition congruences of the overpartition function and cubic partition function and inequalities involving t-core partitions. Concerning q-combinatorics, we establish various combinatorial proofs for q-series identities appearing in Ramanujan's lost notebook and give combinatorial interpretations for third and sixth order mock theta functions.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2010

Author dc:creator

• Kim, Byung Chan

Contributors dc:contributor

• Berndt, Bruce C.
• Ahlgren, Scott
• Zaharescu, Alexandru
• Yong, Alexander

• Partitions
• Partition congruences
• q-series
• Modular forms
• Combinatorial proof
• Mock theta functions

Statement dc:rights

• Copyright 2010 Byung Chan Kim

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/15588

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/15588