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.

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Correspondence to Kevin Ford*.

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

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Ford*, K. Maximal Collections of Intersecting Arithmetic Progressions. Combinatorica 23, 263–281 (2003).

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AMS Subject Classification (2000):

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