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{\bf Randall McCutcheon}
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{\bf The Wildcard Set's Size in the Density Hales-Jewett Theorem}
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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 S\'ark\"ozy's theorem on
square differences in sets of positive upper density.



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