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.
Electronic Journal of Combinatorics
McCutcheon, R. (2011). The wildcard set's size in the density hales-jewett theorem. Electronic Journal of Combinatorics, 18 (1) https://doi.org/10.37236/601