On the asymptotic minimum number of monochromatic 3-term arithmetic progressions
| dc.creator | Parrilo, Pablo A. | |
| dc.creator | Robertson, Aaron | |
| dc.creator | Saracino, Dan | |
| dc.date | 2006-09-19 | |
| dc.date | 2006-09-20 | |
| dc.date.accessioned | 2026-07-07T08:49:47Z | |
| dc.date.available | 2026-07-07T08:49:47Z | |
| dc.description | Let V(n) be the minimum number of monochromatic 3-term arithmetic progressions in any 2-coloring of {1,2,...,n}. We show that (1675/32768) n^2 (1+o(1)) <= V(n) <= (117/2192) n^2(1+o(1)). As a consequence, we find that V(n) is strictly greater than the corresponding number for Schur triples (which is (1/22) n^2 (1+o(1)). Additionally, we disprove the conjecture that V(n) = (1/16) n^2(1+o(1)), as well as a more general conjecture. | |
| dc.description | 9 pages. Revised version fixes formatting errors (same text) | |
| dc.identifier | https://arxiv.org/abs/math/0609532 | |
| dc.identifier | http://arxiv.org/abs/math/0609532 | |
| dc.identifier | Journal of Combinatorial Theory, Series A. Volume 115, Issue 1, January 2008, pp. 185-192. | |
| dc.identifier | doi:10.1016/j.jcta.2007.03.006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144426 | |
| dc.subject | Combinatorics | |
| dc.subject | Optimization and Control | |
| dc.title | On the asymptotic minimum number of monochromatic 3-term arithmetic progressions | |
| dc.type | text |