The Hales-Jewett theorem for alphabet of size 3 states that whenever the Hales-Jewett cube $[3]^{n}$ is $r$-coloured there is a monochromatic line (for n large). Conlon and Kamcev conjectured that, for any $n$, there is a 2-colouring of $[3]^{n}$ for which there is no monochromatic line whose active coordinate set is an interval. In this note we disprove this conjecture.
@article{10_37236_7664,
author = {Imre Leader and Eero R\"aty},
title = {A note on intervals in the {Hales-Jewett} theorem},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {3},
doi = {10.37236/7664},
zbl = {1393.05258},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7664/}
}
TY - JOUR
AU - Imre Leader
AU - Eero Räty
TI - A note on intervals in the Hales-Jewett theorem
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/7664/
DO - 10.37236/7664
ID - 10_37236_7664
ER -
%0 Journal Article
%A Imre Leader
%A Eero Räty
%T A note on intervals in the Hales-Jewett theorem
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/7664/
%R 10.37236/7664
%F 10_37236_7664
Imre Leader; Eero Räty. A note on intervals in the Hales-Jewett theorem. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/7664
