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 Title: Some Results on the Congruential and Gap -Theoretic Study of Partition Functions Author(s): Eichhorn, Dennis Alan Doctoral Committee Chair(s): Berndt, Bruce C. Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics 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. Issue Date: 1999 Type: Text Language: English Description: 102 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999. URI: http://hdl.handle.net/2142/86982 Other Identifier(s): (MiAaPQ)AAI9953007 Date Available in IDEALS: 2015-09-28 Date Deposited: 1999
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