The van der Waerden complex

Richard Ehrenborg, Likith Govindaiah, Peter S. Park, Margaret Readdy
2017 Journal of Number Theory  
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 k / k. Furthermore, we give bounds on n and k which imply that the van der Waerden complex is contractible.
doi:10.1016/j.jnt.2016.08.012 fatcat:vm6zuc3bobhk5frlik56q37si4