Timeline for An inequality involving integer partitions
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Sep 28 at 22:56 | comment | added | Zhi-Wei Sun | @Richard Stanley Thank you for informing me the paper of Szekeres on the asymptotic behavior of $p(n,k)$. This paper might be helpful. | |
| Sep 28 at 15:42 | comment | added | Richard Stanley | An asymptotic estimate for $p(n,k)$ was obtained by G. Szekeres, Some asymptotic formulae in the theory of partitions (II), Quart. J. Math. Oxford 4 (2), 96--111, that implies the unimodality of the sequence $p(n,1), p(n,2), \dots, p(n,n)$. Does this estimate or some refinement of it imply log-concavity? | |
| Sep 28 at 13:55 | history | edited | Zhi-Wei Sun | CC BY-SA 4.0 |
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| Sep 28 at 13:42 | comment | added | Zhi-Wei Sun | @Fedor Petrov. Thank you for pointing out that. | |
| Sep 28 at 10:02 | comment | added | Ilya Bogdanov | It is very decent to cite related results, if you are aware of them. | |
| Sep 28 at 9:31 | comment | added | Fedor Petrov | it worth mention that for fixed $c$ and $n\geqslant 2c$, we have $p(n,n-c)=p(c)$, thus this strengthens the log-concavity of $p(n)$ | |
| Sep 28 at 9:15 | history | asked | Zhi-Wei Sun | CC BY-SA 4.0 |