Timeline for Density of Ramsey subsets of $\omega$
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 26, 2020 at 0:50 | comment | added | bof | To see that "the set of $n$ for which that holds can be arbitrarily sparse" consider a partition of $\omega$ into intervals $I_1\lt I_2\lt\cdots$ of rapidly increasing length and let $f(\{x,y\})=i\in\{0,1,2\}$ if $x,y\in I_{3m+i}$. | |
| Dec 26, 2020 at 0:36 | comment | added | bof | @PéterKomjáth The set can't possibly contain "at least $c\log n$ elements below $n$" for all $n$. What is the correct statement? Is it something like "at least $c\log n$ elements below $n$ for infinitely many $n$"? But the set of $n$ for which that holds can be arbitrarily sparse? | |
| Dec 24, 2020 at 8:20 | comment | added | Péter Komjáth | It is worth mentioning the following result of Erdos and Galvin: in a coloring $f:[\omega]^2\to\{0,1,2\}$ there is an infinite set containing at least $c\log n$ elements below $n$ and spanning only 2 colors. Erdos, Galvin: Some Ramsey type theorems, Disc. Math., 87(1991), 261-269. | |
| Dec 23, 2020 at 13:40 | vote | accept | Dominic van der Zypen | ||
| Dec 23, 2020 at 13:37 | vote | accept | Dominic van der Zypen | ||
| Dec 23, 2020 at 13:40 | |||||
| Dec 23, 2020 at 13:36 | answer | added | Péter Komjáth | timeline score: 9 | |
| Dec 23, 2020 at 13:34 | answer | added | Will Brian | timeline score: 7 | |
| Dec 23, 2020 at 13:09 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |