Two New Extensions of the Hales-Jewett Theorem

: We prove two extensions of the Hales-Jewett coloring theorem. The first is a polynomial version of a finitary case of Furstenberg and Katznelson's multiparameter elaboration of a theorem, due to Carlson, about variable words. The second is an "idempotent" version of a result of Carlson and Simpson. MSC2000: Primary 05D10; Secondary 22A15. For k, N N, let WN k denote the set of length-N words on the alphabet {0, 1,

• Type: Journal
• Year: 2000
• Where: COMBINATORICS
• Authors: Randall McCutcheon
• Keywords: COMBINATORICS 2000, Finitary Case, Polynomial Version, Variable Word