We prove a density version of the Carlson–Simpson Theorem. Specifically we show the following.
For every integer and every set of words over satisfying
there exist a word over and a sequence of left variable words over such that the set
is contained in .
While the result is infinite-dimensional its proof is based on an appropriate finite and quantitative version, also obtained in the paper.
Cite this article
Pandelis Dodos, Vassilis Kanellopoulos, Konstantinos Tyros, A density version of the Carlson–Simpson theorem. J. Eur. Math. Soc. 16 (2014), no. 10, pp. 2097–2164DOI 10.4171/JEMS/484