A combinatorial line in 
is a set of 
words obtained by fixing some coordinate positions and placing
a common variable letter in all remaining positions, with at least one variable position
(Hales and Jewett 1963). Substituting each of the 
letters for the variable gives the members of the line. For
example, in 
,
the words 
,
,
and 
form a combinatorial line.
The density Hales-Jewett theorem guarantees a combinatorial line in every subset of 
of fixed positive density once 
is sufficiently large. For 
, every combinatorial line is a collinear
triple in real Euclidean space, although not every
collinear triple is a combinatorial line.
