Basis partitions and their signature
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914164671250432 |
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| author | Alladi, Krishnaswami |
| author_facet | Alladi, Krishnaswami |
| contents | 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 as complete. Finally we discuss basis partitions and minimal basis partitions among partitions with non-repeating odd parts by representing them using 2-modular graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Basis partitions and their signature Alladi, Krishnaswami Combinatorics Number Theory Primary 05A17, 05A19, Secondary 05A15 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 as complete. Finally we discuss basis partitions and minimal basis partitions among partitions with non-repeating odd parts by representing them using 2-modular graphs. |
| title | Basis partitions and their signature |
| topic | Combinatorics Number Theory Primary 05A17, 05A19, Secondary 05A15 |
| url | https://arxiv.org/abs/2507.14734 |