IDEALS Home University of Illinois at Urbana-Champaign logo The Alma Mater The Main Quad

Arithmetic of partition functions and q-combinatorics

Show simple item record

Bookmark or cite this item: http://hdl.handle.net/2142/15588

Files in this item

File Description Format
PDF Kim_ByungChang.pdf (575KB) (no description provided) PDF
Unknown thesis2.bib (56KB) Reference list in bib format Unknown
Title: Arithmetic of partition functions and q-combinatorics
Author(s): Kim, Byung Chan
Director of Research: Berndt, Bruce C.; Ahlgren, Scott
Doctoral Committee Chair(s): Zaharescu, Alexandru
Doctoral Committee Member(s): Yong, Alexander; Berndt, Bruce C.; Ahlgren, Scott
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(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.
Issue Date: 2010-05-14
URI: http://hdl.handle.net/2142/15588
Rights Information: Copyright 2010 Byung Chan Kim
Date Available in IDEALS: 2010-05-14
2012-05-15
Date Deposited: May 2010
 

This item appears in the following Collection(s)

Show simple item record

Item Statistics

  • Total Downloads: 174
  • Downloads this Month: 6
  • Downloads Today: 0

Browse

My Account

Information

Access Key