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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
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


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