Overpartitions with repeated smallest non-overlined part
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914428638724096 |
|---|---|
| author | Malik, Amita Sarma, Rishabh |
| author_facet | Malik, Amita Sarma, Rishabh |
| contents | Inspired by Andrews' and Bachraoui's work on partitions with repeated smallest part, we extend the concept to overpartitions. We study overpartitions with the restriction that the smallest non-overlined part appears exactly $k$ times and every overlined part is bigger than this part. We prove results expressing the generating functions of these overpartitions (and their subclass where no part has the same parity as the smallest part, among others) as linear combinations of the $q$-Pochhammer symbols with rational functions in $q$ as coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15601 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Overpartitions with repeated smallest non-overlined part Malik, Amita Sarma, Rishabh Combinatorics Number Theory 11P81, 05A15, 05A17, 05A19 Inspired by Andrews' and Bachraoui's work on partitions with repeated smallest part, we extend the concept to overpartitions. We study overpartitions with the restriction that the smallest non-overlined part appears exactly $k$ times and every overlined part is bigger than this part. We prove results expressing the generating functions of these overpartitions (and their subclass where no part has the same parity as the smallest part, among others) as linear combinations of the $q$-Pochhammer symbols with rational functions in $q$ as coefficients. |
| title | Overpartitions with repeated smallest non-overlined part |
| topic | Combinatorics Number Theory 11P81, 05A15, 05A17, 05A19 |
| url | https://arxiv.org/abs/2601.15601 |