Vector Partitions
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...
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ndltd-ETSU-oai-dc.etsu.edu-etd-48372019-05-16T04:57:54Z Vector Partitions French, Jennifer 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. 2018-05-01T07:00:00Z text application/pdf https://dc.etsu.edu/etd/3392 https://dc.etsu.edu/cgi/viewcontent.cgi?article=4837&context=etd Copyright by the authors. Electronic Theses and Dissertations eng Digital Commons @ East Tennessee State University number theory integer partitions vector partitions Discrete Mathematics and Combinatorics Number Theory |
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number theory integer partitions vector partitions Discrete Mathematics and Combinatorics Number Theory |
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number theory integer partitions vector partitions Discrete Mathematics and Combinatorics Number Theory French, Jennifer Vector Partitions |
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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. |
author |
French, Jennifer |
author_facet |
French, Jennifer |
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French, Jennifer |
title |
Vector Partitions |
title_short |
Vector Partitions |
title_full |
Vector Partitions |
title_fullStr |
Vector Partitions |
title_full_unstemmed |
Vector Partitions |
title_sort |
vector partitions |
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Digital Commons @ East Tennessee State University |
publishDate |
2018 |
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https://dc.etsu.edu/etd/3392 https://dc.etsu.edu/cgi/viewcontent.cgi?article=4837&context=etd |
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AT frenchjennifer vectorpartitions |
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1719188748601655296 |