Corpus ID: 118065677

Formulating Szemerédi's Theorem in Terms of Ultrafilters

@article{Zirnstein2012FormulatingST,
  title={Formulating Szemer{\'e}di's Theorem in Terms of Ultrafilters},
  author={Heinrich-Gregor Zirnstein},
  journal={arXiv: Functional Analysis},
  year={2012}
}
  • Heinrich-Gregor Zirnstein
  • Published 2012
  • Mathematics
  • arXiv: Functional Analysis
  • Van der Waerden's theorem asserts that if you color the natural numbers with, say, five different colors, then you can always find arbitrarily long sequences of numbers that have the same color and that form an arithmetic progression. Szemer\'edi's theorem generalizes this statement and asserts that every subset of natural numbers with positive density contains arithmetic progressions of arbitrary length. Van der Waerden's theorem can be proven using elementary combinatorics, but it is also… CONTINUE READING
    1 Citations

    Figures from this paper.

    References

    SHOWING 1-10 OF 12 REFERENCES
    An ultrafilter approach to Jin’s theorem
    • 28
    • PDF
    The sumset phenomenon
    • 54
    • Highly Influential
    • PDF
    Algebra in the Stone-Cech Compactification: Theory and Applications
    • 459
    • Highly Influential
    • PDF
    Handbook of Analysis and Its Foundations
    • 275
    • PDF
    Recurrence in Ergodic Theory and Combinatorial Number Theory
    • 628
    • PDF
    Mass- und Integrationstheorie
    • Springer,
    • 2005
    Beweis einer Baudetschen Vermutung
    • Nieuw. Arch. Wisk
    • 1928
    Princeton landmarks in mathematics and physics
    • Princeton University Press,
    • 1996
    Szemerédi's Theorem
    • 10