Some New Exact van der Waerden Numbers
| dc.creator | Landman, Bruce | |
| dc.creator | Robertson, Aaron | |
| dc.creator | Culver, Clay | |
| dc.date | 2005-07-01 | |
| dc.date.accessioned | 2026-07-07T05:21:18Z | |
| dc.date.available | 2026-07-07T05:21:18Z | |
| dc.description | For positive integers $r,k_0,k_1,...,k_{r-1},$ the van der Waerden number $w(k_0,k_1,...,k_{r-1})$ is the least positive integer $n$ such that whenever $\{1,2,...,n\}$ is partitioned into $r$ sets $S_{0},S_{1},...,S_{r-1}$, there is some $i$ so that $S_i$ contains a $k_i$-term arithmetic progression. We find several new exact values of $w(k_0,k_1,...,k_{r-1})$. In addition, for the situation in which only one value of $k_i$ differs from 2, we give a precise formula for the van der Waerden function (provided this one value of $k_i$ is not too small) | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0507019 | |
| dc.identifier | http://arxiv.org/abs/math/0507019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75645 | |
| dc.subject | Combinatorics | |
| dc.subject | 05D10 | |
| dc.title | Some New Exact van der Waerden Numbers | |
| dc.type | text |