Higher Order Turan Inequalities for the Distinct Partition Function
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910391393583104 |
|---|---|
| author | Dong, Janet J. W. Ji, Kathy Q. |
| author_facet | Dong, Janet J. W. Ji, Kathy Q. |
| contents | We prove that the number $q(n)$ of partitions into distinct parts is log-concave for $n \geq 33$ and satisfies the higher order Turán inequalities for $n\geq 121$ conjectured by Craig and Pun. In doing so, we establish explicit error terms for $q(n)$ and for $q(n-1)q(n+1)/q(n)^2$ based on Chern's asymptotic formulas for $η$-quotients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_05243 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Higher Order Turan Inequalities for the Distinct Partition Function Dong, Janet J. W. Ji, Kathy Q. Combinatorics Number Theory We prove that the number $q(n)$ of partitions into distinct parts is log-concave for $n \geq 33$ and satisfies the higher order Turán inequalities for $n\geq 121$ conjectured by Craig and Pun. In doing so, we establish explicit error terms for $q(n)$ and for $q(n-1)q(n+1)/q(n)^2$ based on Chern's asymptotic formulas for $η$-quotients. |
| title | Higher Order Turan Inequalities for the Distinct Partition Function |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2303.05243 |