University of Illinois Urbana-Champaign

Some Results on the Congruential and Gap -Theoretic Study of Partition Functions

Eichhorn, Dennis Alan

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Description

Title
Some Results on the Congruential and Gap -Theoretic Study of Partition Functions
Author(s)
Eichhorn, Dennis Alan
Issue Date
1999
Doctoral Committee Chair(s)
Berndt, Bruce C.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
"Recently, several authors have been treating partitions by considering the gaps between their consecutive parts. Many of the existing results involving ""partitions with parts in the gaps"" bear a striking resemblance to certain weighted partition identities that also arise from the gaps of partitions. In this thesis, we provide combinatorial proofs of several results from the literature involving partitions with parts in the gaps, and in doing so, we discover many generalizations of these original results. Furthermore, we show that these generalizations have several weighted partition identities from the literature as corollaries."
Graduation Semester
1999
Type of Resource
text
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http://hdl.handle.net/2142/86982

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