Basis Partitions and Their Signature
Basis partitions are minimal partitions corresponding to successive rank vectors. We show combinatorially how basis partitions can be generated from primary partitions, which are equivalent to the Rogers-Ramanujan partitions. This leads to the definition of a signature of a basis partition that we u...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2025 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/214178 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Basis Partitions and Their Signature. Krishnaswami Alladi. SIGMA 21 (2025), 104, 17 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862731649734672384 |
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| author | Alladi, Krishnaswami |
| author_facet | Alladi, Krishnaswami |
| citation_txt | Basis Partitions and Their Signature. Krishnaswami Alladi. SIGMA 21 (2025), 104, 17 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Basis partitions are minimal partitions corresponding to successive rank vectors. We show combinatorially how basis partitions can be generated from primary partitions, which are equivalent to the Rogers-Ramanujan partitions. This leads to the definition of a signature of a basis partition that we use to explain certain parity results. We then study a special class of basis partitions, which we term complete. Finally, we discuss basis partitions and minimal basis partitions among partitions with non-repeating odd parts by representing them using 2-modular graphs.
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| first_indexed | 2026-03-21T19:10:03Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214178 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T19:10:03Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Alladi, Krishnaswami 2026-02-20T07:52:55Z 2025 Basis Partitions and Their Signature. Krishnaswami Alladi. SIGMA 21 (2025), 104, 17 pages 1815-0659 2020 Mathematics Subject Classification: 05A17; 05A19; 05A15 arXiv:2507.14734 https://nasplib.isofts.kiev.ua/handle/123456789/214178 https://doi.org/10.3842/SIGMA.2025.104 Basis partitions are minimal partitions corresponding to successive rank vectors. We show combinatorially how basis partitions can be generated from primary partitions, which are equivalent to the Rogers-Ramanujan partitions. This leads to the definition of a signature of a basis partition that we use to explain certain parity results. We then study a special class of basis partitions, which we term complete. Finally, we discuss basis partitions and minimal basis partitions among partitions with non-repeating odd parts by representing them using 2-modular graphs. This work, which was begun in 2007, was completed only in Fall 2013 when I visited The Pennsylvania State University, at which time the results of Section 9 were established. I would like to thank George Andrews for arranging that visit and for urging me to write this manuscript, which was long overdue. But this paper remained unpublished since 2013. I thank Gaurav Bhatnagar, Frank Garvan, Christian Krattenthaler, and Michael Schlosser for including this paper in the special volume of SIGMA in honor of Steve Milne’s 75th birthday. Finally, I thank the referees for their careful reading of the manuscript and for their helpful suggestions. Research supported in part by NSA Grants MSPF-06G-150 and MSPF-08G-154. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Basis Partitions and Their Signature Article published earlier |
| spellingShingle | Basis Partitions and Their Signature Alladi, Krishnaswami |
| title | Basis Partitions and Their Signature |
| title_full | Basis Partitions and Their Signature |
| title_fullStr | Basis Partitions and Their Signature |
| title_full_unstemmed | Basis Partitions and Their Signature |
| title_short | Basis Partitions and Their Signature |
| title_sort | basis partitions and their signature |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214178 |
| work_keys_str_mv | AT alladikrishnaswami basispartitionsandtheirsignature |