Van Der Waerden's Theorem: Exposition and Generalizations

@inproceedings{Gasarch2007VanDW,
  title={Van Der Waerden's Theorem: Exposition and Generalizations},
  author={William Gasarch},
  year={2007}
}
as a, a + p1(d), a + p2(d), . . . , a + pk−1(d) where pi(d) = id. Why these functions? We ponder replacing pi with other functions. The following remarkable theorem was first proved by Bergelson and Leibman [1]. They proved it by first proving the polynomial version of the Hales-Jewitt Theorem [2] (see Section 4 for a statement and proof of the original… CONTINUE READING