The van der Waerden complex

Richard Ehrenborg, Likith Govindaiah, Peter S. Park, Margaret Readdy

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We introduce the van der Waerden complex vdW(n,k) defined as the simplicial complex whose facets correspond to arithmetic progressions of length k in the vertex set {1,2,…,n}. We show the van der Waerden complex vdW(n,k) is homotopy equivalent to a CW-complex whose cells asymptotically have dimension at most log⁡k/log⁡log⁡k. Furthermore, we give bounds on n and k which imply that the van der Waerden complex is contractible.

Original languageEnglish
Pages (from-to)287-300
Number of pages14
JournalJournal of Number Theory
StatePublished - Mar 1 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.


  • Arithmetic progressions
  • Discrete Morse theory
  • Van der Waerden complex

ASJC Scopus subject areas

  • Algebra and Number Theory


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