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@article{FK89,

 title={A density version of the {H}ales-{J}ewett {T}heorem for $k = 3$},
 author={Hillel Furstenberg and Yitzhak Katznelson},
 journal={Discrete Mathematics},
 volume={75},
 pages={227--241},
 year={1989}

}

@article{FK91,

 title={A density version of the {H}ales-{J}ewett {T}heorem},
 author={Hillel Furstenberg and Yitzhak Katznelson},
 journal={Journal d'Analyse Mathematique},
 volume={57},
 pages={64--119},
 year={1991}

}

@article{GRS99,

 title={Extremal problems for sets forming {B}oolean algebras and complete partite hypergraphs},
 author={David S. Gunderson and Vojt{\v{e}}ch R{\"o}dl and Alexander Sidorenko},
 journal={Journal of Combinatorial Theory, Series A},
 volume={88},
 number={2},
 pages={342--367},
 year={1999},

}

@article{HJ63,

 title={Regularity and positional games},
 author={Alfred W. Hales and Robert I. Jewett},
 journal={Transactions of the American Mathematical Society},
 volume={106},
 number={2},
 pages={222--229},
 year={1963},
 publisher={American Mathematical Society}

}

@article{Lub66,

 title = {A short proof of {S}perner's lemma},
 author = {David Lubell},
 journal = {Journal of Combinatorial Theory},
 volume = 1,
 number = 2,
 pages = 299,
 year = 1966,

}

@book{Rei89,

title =       {Approximate distributions of order statistics},
author =      {Rolf-Dieter Reiss},
publisher =   {Springer-Verlag},
year = 1989

}

@article{Spe28,

 title = {Ein {S}atz \"uber {U}ntermengen einer endlichen {M}enge},
 author = {Emanuel Sperner},
 journal = {Mathematische Zeitschrift},
 volume = 27,
 number = 1,
 pages = {544--548},
 year = 1928

}

@incollection{Spe90,

 author = {Joel Spencer},
 title = {The probabilistic lens: {S}perner, {T}ur\'an and {B}regman revisited},
 booktitle = {A tribute to Paul Erd\"{o}s},
 publisher = {Cambridge University Press},
 year = 1990,
 pages = {391--396}

}

@article{Sze75,

 title = {On sets of integers containing no $k$ elements in arithmetic progression},
 author = {Endre Szemer\'edi},
 journal = {Acta Arithmetica},
 volume = {27},
 pages = {199--245},
 year = 1975

}

@article{vdW27,

 title = {Beweis einer {Baudetschen} {Vermutung}},
 author = {Bartel L. van der Waerden},
 journal = {Nieuw Archief voor Wiskunde},
 volume = {15},
 pages = {212--216},
 year = 1927

}