Avoiding Monochromatic Sequences With Special Gaps
| dc.creator | Landman, Bruce M. | |
| dc.creator | Robertson, Aaron | |
| dc.date | 2003-02-04 | |
| dc.date.accessioned | 2026-07-07T04:54:54Z | |
| dc.date.available | 2026-07-07T04:54:54Z | |
| dc.description | For $S$ a set of positive integers, and $k$ and $r$ fixed positive integers, denote by $f(S,k;r)$ the least positive integer $n$ (if it exists) such that within every $r$-coloring of $\{1,2,...,n\}$ there must be a monochromatic sequence $\{x_{1},x_{2},...,x_{k}\}$ with $x_{i}-x_{i-1} \in S$ for $2 \leq i \leq k$. We consider the existence of $f(S,k;r)$ for various choices of $S$, as well as upper and lower bounds on this function. In particular, we show that this function exists for all $k$ if $S$ is an odd translate of the set of primes and $r=2$. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0302041 | |
| dc.identifier | http://arxiv.org/abs/math/0302041 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66441 | |
| dc.subject | Combinatorics | |
| dc.subject | 05D10; 11B25; 11N13 | |
| dc.title | Avoiding Monochromatic Sequences With Special Gaps | |
| dc.type | text |