Factor-complement partitions of ascending k-parameter words

AbstractIn this paper variations of the ∗-version of the Hales-Jewett theorem by Voigt for arbitrary ascending parameter words are used to prove versions of the Hales-Jewett and Graham-Rothschild theorems where every factor of every word is coloured. To facilitate the proof three-alphabet ascending parameter words are introduced. Primitive recursive bounds are given for all new results