Monochromatic boxes in colored grids

Simple item page
dc.creatorCooper, Joshua
dc.creatorFenner, Stephen
dc.creatorPurewal, Semmy
dc.date2008-10-16
dc.date.accessioned2026-07-07T10:10:52Z
dc.date.available2026-07-07T10:10:52Z
dc.descriptionA $d$-dimensional grid is a set of the form $R = [a_1] \times ... \times [a_d]$. A $d$-dimensional box is a set of the form $\{b_1,c_1\} \times ... \times \{b_d,c_d\}$. When a grid is $c$-colored, must it admit a monochromatic box? If so, we say that $R$ is $c$-guaranteed. This question is a relaxation of one attack on bounding the van der Waerden numbers, and also arises as a natural hypergraph Ramsey problem (viz. the Ramsey numbers of hyperoctahedra). We give conditions on the $a_i$ for $R$ to be $c$-guaranteed that are asymptotically tight, and analyze the set of minimally $c$-guaranteed grids.
dc.description17 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/0810.3019
dc.identifierhttp://arxiv.org/abs/0810.3019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171721
dc.subjectCombinatorics
dc.subject05D10
dc.titleMonochromatic boxes in colored grids
dc.typetext

Files

Collections

arXiv