On the degree of regularity of generalized van der Waerden triples
| dc.creator | Frantzikinakis, Nikos | |
| dc.creator | Landman, Bruce | |
| dc.creator | Robertson, Aaron | |
| dc.date | 2005-07-28 | |
| dc.date.accessioned | 2026-07-07T05:22:05Z | |
| dc.date.available | 2026-07-07T05:22:05Z | |
| dc.description | Let $1 \leq a \leq b$ be integers. A triple of the form $(x,ax+d,bx+2d)$, where $x,d$ are positive integers is called an {\em (a,b)-triple}. The {\em degree of regularity} of the family of all $(a,b)$-triples, denoted dor($a,b)$, is the maximum integer $r$ such that every $r$-coloring of $\mathbb{N}$ admits a monochromatic $(a,b)$-triple. We settle, in the affirmative, the conjecture that dor$(a,b) < \infty$ for all $(a,b) \neq (1,1)$. We also disprove the conjecture that dor($a,b) \in \{1,2,\infty\}$ for all $(a,b)$. | |
| dc.description | 5 pages | |
| dc.identifier | https://arxiv.org/abs/math/0507588 | |
| dc.identifier | http://arxiv.org/abs/math/0507588 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75926 | |
| dc.subject | Combinatorics | |
| dc.subject | 05D10 | |
| dc.title | On the degree of regularity of generalized van der Waerden triples | |
| dc.type | text |