Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

5-2018

Committee Chair or Co-Chairs

Rodney Keaton

Committee Members

Robert A. Beeler, Anant Godbole

Abstract

Integer partitions have been studied by many mathematicians over hundreds of years. Many identities exist between integer partitions, such as Euler’s discovery that every number has the same amount of partitions into distinct parts as into odd parts. These identities can be proven using methods such as conjugation or generating functions. Over the years, mathematicians have worked to expand partition identities to vectors. In 1963, M. S. Cheema proved that every vector has the same number of partitions into distinct vectors as into vectors with at least one component odd. This parallels Euler’s result for integer partitions. The primary purpose of this paper is to use generating functions to prove other vector partition identities that parallel results of integer partitions.

Document Type

Thesis - Open Access

Copyright

Copyright by the authors.

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