Thick set

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.

ee also

*Syndetic set
*Piecewise syndetic set
*Ergodic Ramsey theory
*Cofinite set
*Cofinal set

References

* J. McLeod, " [http://www.mtholyoke.edu/%7Ejmcleod/somenotionsofsize.pdf Some Notions of Size in Partial Semigroups] ", "Topology Proceedings", Vol. 25 (2000), pp. 317-332.
* V. Bergelson, " [http://www.math.ohio-state.edu/~vitaly/vbkatsiveli20march03.pdf 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)
* V. Bergelson, N. Hindman, " [http://members.aol.com/nhfiles2/pdf/large.pdf Partition regular structures contained in large sets are abundant] ", "J. Comb. Theory (Series A)" 93 (2001), pp. 18-36


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  • thick|set — thick set or thick|set «THIHK SEHT», adjective, noun. –adj. 1. growing or occurring closely together; thickly set: »a thick set hedge. 2. thick in form or build: »a short, thick set man. –n. 1. = thicket. (Cf. ↑thicket) …   Useful english dictionary

  • thick-set — or thick|set «THIHK SEHT», adjective, noun. –adj. 1. growing or occurring closely together; thickly set: »a thick set hedge. 2. thick in form or build: »a short, thick set man. –n. 1. = thicket. (Cf. ↑thicket) 2. a thick hedg …   Useful english dictionary

  • thick-set — see thickset …   English dictionary

  • thick·set — …   Useful english dictionary

  • Thick — can refer to:* Thick description of human behavior * Thick set, a set of integers * Thick Records, a record label * Thick Physique * A thick , someone lacking in intelligence. Stupid person …   Wikipedia

  • Thick as a Brick — Студийный альбом Jethro Tull …   Википедия

  • Thick — (th[i^]k), a. [Compar. {Thicker} ( [ e]r); superl. {Thickest}.] [OE. thicke, AS. [thorn]icce; akin to D. dik, OS. thikki, OHG. dicchi thick, dense, G. dick thick, Icel. [thorn]ykkr, [thorn]j[ o]kkr, and probably to Gael. & Ir. tiugh. Cf.… …   The Collaborative International Dictionary of English

  • Thick register — Thick Thick (th[i^]k), a. [Compar. {Thicker} ( [ e]r); superl. {Thickest}.] [OE. thicke, AS. [thorn]icce; akin to D. dik, OS. thikki, OHG. dicchi thick, dense, G. dick thick, Icel. [thorn]ykkr, [thorn]j[ o]kkr, and probably to Gael. & Ir. tiugh.… …   The Collaborative International Dictionary of English

  • Thick stuff — Thick Thick (th[i^]k), a. [Compar. {Thicker} ( [ e]r); superl. {Thickest}.] [OE. thicke, AS. [thorn]icce; akin to D. dik, OS. thikki, OHG. dicchi thick, dense, G. dick thick, Icel. [thorn]ykkr, [thorn]j[ o]kkr, and probably to Gael. & Ir. tiugh.… …   The Collaborative International Dictionary of English

  • Thick Black Theory — is a philosophical treatise written by Li Zhongwu (1879 1944) [ [http://translate.google.com/translate?hl=en sl=ko u=http://blog.joins.com/media/folderListSlide.asp%3Fuid%3Dchrest%26folder%3D44%26list id%3D7474376 sa=X oi=translate resnum=1… …   Wikipedia

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