English

On a Generalization of the van der Waerden Theorem

Combinatorics 2007-05-23 v1

Abstract

For a given length and a given degree and an arbitrary partition of the positive integers, there always is a cell containing a polynomial progression of that length and that degree; moreover, the coefficients of the generating polynomial can be chosen from a given semigroup and one can prescribe the occurring powers. A multidimensional version is included.

Keywords

Cite

@article{arxiv.math/0703839,
  title  = {On a Generalization of the van der Waerden Theorem},
  author = {Rudi Hirschfeld},
  journal= {arXiv preprint arXiv:math/0703839},
  year   = {2007}
}

Comments

5 pages

R2 v1 2026-07-22T17:53:21.831Z