Thick set

In mathematics, a thick set is a set of integers that contains arbitrarily long intervals. That is, given a thick set $T$, for every $p \in \mathbb{N}$, there is some $n \in \mathbb{N}$ such that $\{n, n+1, n+2, ... , n+p \} \subset T$.

See also

• Cofinal (mathematics)
• Cofiniteness
• Ergodic Ramsey theory
• Piecewise syndetic set
• Syndetic set

References

• J. McLeod, "Some Notions of Size in Partial Semigroups", Topology Proceedings, Vol. 25 (2000), pp. 317-332.
• Vitaly Bergelson, "Minimal Idempotents and Ergodic Ramsey Theory", Topics in Dynamics and Ergodic Theory 8-39, London Math. Soc. Lecture Note Series 310, Cambridge Univ. Press, Cambridge, (2003)
• Vitaly Bergelson, N. Hindman, "Partition regular structures contained in large sets are abundant", J. Comb. Theory (Series A) 93 (2001), pp. 18-36