Maximal Collections of Intersecting Arithmetic Progressions

Let N t (k) be the maximum number of k-term arithmetic progressions of real numbers, any two of which have t points in common. We determine N 2(k) for prime k and all large k, and give upper and lower bounds for N t (k) when t ≥ 3.

This is a preview of subscription content, access via your institution.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Kevin Ford*.

Additional information

* Research supported in part by NSF grant DMS-0070618.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ford*, K. Maximal Collections of Intersecting Arithmetic Progressions. Combinatorica 23, 263–281 (2003). https://doi.org/10.1007/s00493-003-0021-4

Download citation

AMS Subject Classification (2000):

  • 05D05
  • 11B75
  • 11B25
  • 11A05
  • 11N05
  • 11N37