On the restricted $k$-multipartition function
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916111661924352 |
|---|---|
| author | Cimpoeas, Mircea Teodor, Alexandra |
| author_facet | Cimpoeas, Mircea Teodor, Alexandra |
| contents | Let $\mathbf a=(a_1,\ldots,a_r)$ be a sequence of positive integers and $k\geq 2$ an integer. We study $p_{k,\mathbf a}(n)$, the restricted $k$-multipartition function associated to $\mathbf a$ and $k$. We prove new formulas for $p_{k,\mathbf a}(n)$, its waves $W_j(n,k,\mathbf a)$'s and its polynomial part $P_{k,\mathbf a}(n)$. Also, we give a lower bound for the density of the set $\{n\geq 0\;:\;p_{k,\mathbf a}(n)\not\equiv 0(\bmod\;m)\}$, where $m\geq 2$ is an integer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00057 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the restricted $k$-multipartition function Cimpoeas, Mircea Teodor, Alexandra Number Theory Combinatorics 11P81, 11P83 Let $\mathbf a=(a_1,\ldots,a_r)$ be a sequence of positive integers and $k\geq 2$ an integer. We study $p_{k,\mathbf a}(n)$, the restricted $k$-multipartition function associated to $\mathbf a$ and $k$. We prove new formulas for $p_{k,\mathbf a}(n)$, its waves $W_j(n,k,\mathbf a)$'s and its polynomial part $P_{k,\mathbf a}(n)$. Also, we give a lower bound for the density of the set $\{n\geq 0\;:\;p_{k,\mathbf a}(n)\not\equiv 0(\bmod\;m)\}$, where $m\geq 2$ is an integer. |
| title | On the restricted $k$-multipartition function |
| topic | Number Theory Combinatorics 11P81, 11P83 |
| url | https://arxiv.org/abs/2402.00057 |