Geodesic
The wildcard set's size in the density Hales-Jewett theorem
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/601
Classification : 05D10, 11B25
Mots-clés : Sárközy's theorem on square differences in sets of positive upper density 
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     author = {Randall McCutcheon},
     title = {The wildcard set's size in the density {Hales-Jewett} theorem},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/601},
     zbl = {1233.05195},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/601/}
}
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Randall McCutcheon. The wildcard set's size in the density Hales-Jewett theorem. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/601

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