Ramsey Theory for Words over an Infinite Alphabet

Details Ramsey Theory for Words over an Infinite Alphabet Ramsey Theory for Words over an Infinite Alphabet

2009-04-13

arxiv.org/abs/0904.1948v1

Mathematics

Combinatorics

Scientific paper

A complete partition theory is presented for omega-located words (and omega-words), namely for located words over an infinite alphabet dominated by a fixed increasing sequence. This theory strengthens in an essential way the classical Carlson, Furstenberg-Katznelson, and Bergelson-Blass-Hindman partition theory for words over a finite alphabet. Consequences of this theory are strong simultaneous extensions of the classical Hindman, Milliken-Taylor partition theorem, and of a van der Waerden theorem for general semigroups, extending results of Hindman-Strauss and Beiglbock.

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