Timeline for What are the best known bounds on the number of partitions of $n$ into exactly $k$ distinct parts?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 9, 2011 at 17:49 | comment | added | Gerhard Paseman | Cool! I suspected something like that, but it helps a lot to see your phrasing of it. Thanks, Gerry! Gerhard "Ask Me About System Design" Paseman, 2011.08.09 | |
| Aug 9, 2011 at 17:29 | answer | added | Rob | timeline score: 2 | |
| Aug 9, 2011 at 5:47 | comment | added | Gerry Myerson | @Gerhard, I mean the number of partitions is $C_kn^{k-1}+O(n^{k-2})$. See also Igor Rivin's answer. What actually happens is that for each $k$ there's an $m=m(k)$ such that there are $m$ polynomials $P_i(x)$ such that if $n\equiv i\pmod m$ then the number of partitions is $P_i(n)$; each $P_i$ has as its leading term the term given in Igor's answer. | |
| Aug 9, 2011 at 4:35 | vote | accept | Rob | ||
| Aug 9, 2011 at 4:05 | comment | added | Gerhard Paseman | Gerry, does this mean that there is a polynomial p(n) such that (for a specified k) the number of partitions of n into exactly k parts is p(n)? I suspect you mean the latter, which is that there are polynomials p(n) and q(n) which serve as upper and lower bounds (when n is sufficiently large) to the desired function. Some clarity would be appreciated. Gerhard "Ask Me About System Design" Paseman, 2011.08.08 | |
| Aug 9, 2011 at 1:44 | answer | added | Igor Rivin | timeline score: 6 | |
| Aug 9, 2011 at 1:35 | comment | added | Gerry Myerson | For a fixed $k$, the number of partitions of $n$ into $k$ parts grows as a polynomial in $n$, of degree $k-1$. | |
| Aug 9, 2011 at 1:22 | history | asked | Rob | CC BY-SA 3.0 |