Syndetic set explained

In mathematics, a syndetic set is a subset of the natural numbers having the property of "bounded gaps": that the sizes of the gaps in the sequence of natural numbers is bounded.

Definition

A set

S \sub N is called syndetic if for some finite subset F of N c up _{n} (S - n) = N

where

S - n = \{m \in N : m + n \in S \} . Thus syndetic sets have "bounded gaps"; for a syndetic set S , there is an integer p = p(S) such that [a, a +1 , a +2 , ... , a + p] c ap S ≠ \emptyset for any a \in N .

See also

• Ergodic Ramsey theory
  • Piecewise syndetic set Thick set

References

• McLeod . Jillian. Some Notions of Size in Partial Semigroups. Topology Proceedings. 25. Summer 2000. 2000. 317—332.
• Book: Bergelson . Vitaly . Vitaly Bergelson. Minimal Idempotents and Ergodic Ramsey Theory. Topics in Dynamics and Ergodic Theory. 8—39. London Mathematical Society Lecture Note Series. 310. Cambridge University Press, Cambridge. 2003. 10.1017/CBO9780511546716.004. http://www.math.ohio-state.edu/~vitaly/vbkatsiveli20march03.pdf.
• Bergelson . Vitaly . Vitaly Bergelson . Hindman . Neil . Neil Hindman . Partition regular structures contained in large sets are abundant . . Series A . 93 . 1 . 2001 . 18—36 . 10.1006/jcta.2000.3061 . free.