A generalisation of two partition theorems of Andrews
In 1968 and 1969, Andrews proved two partition theorems of the Rogers-Ramanujan type which generalise Schur’s celebrated partition identity (1926). Andrews’ two generalisations of Schur’s theorem went on to become two of the most influential results in the theory of partitions, finding applications...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2015-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2529/pdf |
| _version_ | 1797270192486612992 |
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| author | Jehanne Dousse |
| author_facet | Jehanne Dousse |
| author_sort | Jehanne Dousse |
| collection | DOAJ |
| description | In 1968 and 1969, Andrews proved two partition theorems of the Rogers-Ramanujan type which generalise Schur’s celebrated partition identity (1926). Andrews’ two generalisations of Schur’s theorem went on to become two of the most influential results in the theory of partitions, finding applications in combinatorics, representation theory and quantum algebra. In this paper we generalise both of Andrews’ theorems to overpartitions. The proofs use a new technique which consists in going back and forth from $q$-difference equations on generating functions to recurrence equations on their coefficients. |
| first_indexed | 2024-04-25T02:00:22Z |
| format | Article |
| id | doaj.art-294dadd51ec74a428cfd1edb14c9d32c |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:22Z |
| publishDate | 2015-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-294dadd51ec74a428cfd1edb14c9d32c2024-03-07T15:01:26ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502015-01-01DMTCS Proceedings, 27th...Proceedings10.46298/dmtcs.25292529A generalisation of two partition theorems of AndrewsJehanne Dousse0Laboratoire d'informatique Algorithmique : Fondements et ApplicationsIn 1968 and 1969, Andrews proved two partition theorems of the Rogers-Ramanujan type which generalise Schur’s celebrated partition identity (1926). Andrews’ two generalisations of Schur’s theorem went on to become two of the most influential results in the theory of partitions, finding applications in combinatorics, representation theory and quantum algebra. In this paper we generalise both of Andrews’ theorems to overpartitions. The proofs use a new technique which consists in going back and forth from $q$-difference equations on generating functions to recurrence equations on their coefficients.https://dmtcs.episciences.org/2529/pdfinteger partitionsoverpartitions$q$-difference equationsrecurrences[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Jehanne Dousse A generalisation of two partition theorems of Andrews Discrete Mathematics & Theoretical Computer Science integer partitions overpartitions $q$-difference equations recurrences [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | A generalisation of two partition theorems of Andrews |
| title_full | A generalisation of two partition theorems of Andrews |
| title_fullStr | A generalisation of two partition theorems of Andrews |
| title_full_unstemmed | A generalisation of two partition theorems of Andrews |
| title_short | A generalisation of two partition theorems of Andrews |
| title_sort | generalisation of two partition theorems of andrews |
| topic | integer partitions overpartitions $q$-difference equations recurrences [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2529/pdf |
| work_keys_str_mv | AT jehannedousse ageneralisationoftwopartitiontheoremsofandrews AT jehannedousse generalisationoftwopartitiontheoremsofandrews |