The wildcard set's size in the density hales-jewett theorem


In this paper prove results concerning restrictions on the cardinality of the wildcard set in the density Hales-Jewett theorem, establishing in particular that for general k one may choose this cardinality from any IP set and that for k = 2 it may be chosen to be a square, thus providing an abstract extension of Sárközy's theorem on square differences in sets of positive upper density.

Publication Title

Electronic Journal of Combinatorics