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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
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
Rights Information: Copyright 2010 Byung Chan Kim
Date Available in IDEALS: 2010-05-14
Date Deposited: May 2010

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