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480:. London Mathematical Society Lecture Note Series. Vol. 310. Cambridge University Press, Cambridge. pp. 8–39.
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having the property of "bounded gaps": that the sizes of the gaps in the sequence of natural numbers is bounded.
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502:"Partition regular structures contained in large sets are abundant"
242:. Thus syndetic sets have "bounded gaps"; for a syndetic set
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168:{\displaystyle \bigcup _{n\in F}(S-n)=\mathbb {N} }
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235:{\displaystyle S-n=\{m\in \mathbb {N} :m+n\in S\}}
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471:"Minimal Idempotents and Ergodic Ramsey Theory"
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448:"Some Notions of Size in Partial Semigroups"
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379:{\displaystyle \bigcap S\neq \emptyset }
478:Topics in Dynamics and Ergodic Theory
64:{\displaystyle S\subset \mathbb {N} }
16:Type of subset of the natural numbers
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407:{\displaystyle a\in \mathbb {N} }
507:Journal of Combinatorial Theory
71:is called syndetic if for some
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486:10.1017/CBO9780511546716.004
110:{\displaystyle \mathbb {N} }
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446:McLeod, Jillian (2000).
461:(Summer 2000): 317–332.
521:10.1006/jcta.2000.3061
429:Piecewise syndetic set
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293:{\displaystyle p=p(S)}
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424:Ergodic Ramsey theory
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494:Bergelson, Vitaly
467:Bergelson, Vitaly
255:{\displaystyle S}
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88:{\displaystyle F}
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539:Semigroup theory
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514:(1): 18–36.
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510:. Series A.
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25:syndetic set
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21:mathematics
533:Categories
440:References
300:such that
39:Definition
434:Thick set
397:∈
374:∅
371:≠
365:⋂
224:∈
204:∈
189:−
149:−
135:∈
128:⋃
54:⊂
500:(2001).
469:(2003).
418:See also
386:for any
264:integer
75:subset
31:of the
178:where
73:finite
43:A set
29:subset
474:(PDF)
451:(PDF)
27:is a
23:, a
516:doi
482:doi
95:of
19:In
535::
512:93
504:.
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476:.
459:25
457:.
453:.
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524:.
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484::
401:N
394:a
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362:]
359:p
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347:.
344:.
341:.
338:,
335:2
332:+
329:a
326:,
323:1
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308:[
288:)
285:S
282:(
279:p
276:=
273:p
250:S
230:}
227:S
221:n
218:+
215:m
212::
208:N
201:m
198:{
195:=
192:n
186:S
162:N
158:=
155:)
152:n
146:S
143:(
138:F
132:n
104:N
83:F
58:N
51:S
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