Séminaire Lotharingien de Combinatoire, B14Se (1986), 2 p.
Giuseppe Pirillo
On Hales-Jewett's Theorem
Abstract.
We prove that, for every finite semigroup S, there exist elements
a1,a2,...,ak,ak+1 of S and integers
i1,i2,...,ik
such that
a1 . xi1 .
a2 . xi2 ...
ak .
xik . ak+1=
a1 . yi1 .
a2 . yi2 ...
ak .
yik . ak+1
for each x,y of S.
The following versions are available: