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.


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