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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Density Hales-Jewett and Moser Numbers
verfasst von : D. H. J. Polymath
Erschienen in: An Irregular Mind
Verlag: Springer Berlin Heidelberg
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For any n ≥ 0 and k ≤ 1, the density Hales-Jewett number cn,k is defined as the size of the largest subset of the cube [k]n:=
1,..., k
n which contains no combinatorial line; similarly, the Moser number c
nk
is the largest subset of the cube [k]n which contains no geometric line. A deep theorem of Furstenberg and Katznelson [11], [12], [19] shows that
c
n,k
=
o
(
k
n
) as
n
→∞ (which implies a similar claim for c
n
); this is already non-trivial for k = 3. Several new proofs of this result have also been recently established [23], [2].