Arithmetic of partition functions and q-combinatorics

Kim, Byung Chan

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https://hdl.handle.net/2142/15588 Copy

Description

Title

Arithmetic of partition functions and q-combinatorics

Author(s)

Kim, Byung Chan

Issue Date

2010-05-14T20:51:42Z

Director of Research (if dissertation) or Advisor (if thesis)

• Berndt, Bruce C.
• Ahlgren, Scott

Doctoral Committee Chair(s)

Zaharescu, Alexandru

Committee Member(s)

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

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

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

Abstract

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.

Graduation Semester

2010-5

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

Copyright and License Information

Copyright 2010 Byung Chan Kim

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