Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts
We give combinatorial interpretations of two residual cranks of overpartitions defined by Bringmann, Lovejoy, and Osburn in 2009, analogous to the crank of partitions given by Andrews and the first author in 1988. As a consequence, we give new versions of their definitions without adjusted weights....
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2024 |
| ISSN: | 1815-0659 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212647 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts. Frank G. Garvan and Rishabh Sarma. SIGMA 20 (2024), 097, 14 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862712272374202368 |
|---|---|
| author | Garvan, Frank G. Sarma, Rishabh |
| author_facet | Garvan, Frank G. Sarma, Rishabh |
| citation_txt | Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts. Frank G. Garvan and Rishabh Sarma. SIGMA 20 (2024), 097, 14 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We give combinatorial interpretations of two residual cranks of overpartitions defined by Bringmann, Lovejoy, and Osburn in 2009, analogous to the crank of partitions given by Andrews and the first author in 1988. As a consequence, we give new versions of their definitions without adjusted weights. Furthermore, we investigate the combinatorial interpretation of an ₂-crank of partitions without repeated odd parts and explore connections of these statistics with their companion rank counterparts and the tenth-order mock theta functions of Ramanujan.
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| first_indexed | 2026-03-19T18:13:26Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212647 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T18:13:26Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Garvan, Frank G. Sarma, Rishabh 2026-02-09T09:32:52Z 2024 Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts. Frank G. Garvan and Rishabh Sarma. SIGMA 20 (2024), 097, 14 pages 1815-0659 2020 Mathematics Subject Classification: 05A15; 05A17; 05A30; 11P81 arXiv:2406.12049 https://nasplib.isofts.kiev.ua/handle/123456789/212647 https://doi.org/10.3842/SIGMA.2024.097 We give combinatorial interpretations of two residual cranks of overpartitions defined by Bringmann, Lovejoy, and Osburn in 2009, analogous to the crank of partitions given by Andrews and the first author in 1988. As a consequence, we give new versions of their definitions without adjusted weights. Furthermore, we investigate the combinatorial interpretation of an ₂-crank of partitions without repeated odd parts and explore connections of these statistics with their companion rank counterparts and the tenth-order mock theta functions of Ramanujan. We thank the referees for their comments and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts Article published earlier |
| spellingShingle | Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts Garvan, Frank G. Sarma, Rishabh |
| title | Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts |
| title_full | Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts |
| title_fullStr | Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts |
| title_full_unstemmed | Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts |
| title_short | Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts |
| title_sort | combinatorial interpretations of cranks of overpartitions and partitions without repeated odd parts |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212647 |
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