Existence thresholds and Ramsey properties of random posets

Let P(n) denote the power set of [n], ordered by inclusion, and let P(n,p) denote the random poset obtained from P(n) by retaining each element from P(n) independently at random with probability p and discarding it otherwise. Given any fixed poset F we determine the threshold for the property that P...

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Bibliographic Details
Published in:Random structures & algorithms 2020-12, Vol.57 (4), p.1097-1133
Main Authors: Falgas‐Ravry, Victor, Markström, Klas, Treglown, Andrew, Zhao, Yi
Format: Article
Language:English
Subjects:
boolean lattice
existence thresholds
Ramsey properties
random posets
Set theory
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Summary:Let P(n) denote the power set of [n], ordered by inclusion, and let P(n,p) denote the random poset obtained from P(n) by retaining each element from P(n) independently at random with probability p and discarding it otherwise. Given any fixed poset F we determine the threshold for the property that P(n,p) contains F as an induced subposet. We also asymptotically determine the number of copies of a fixed poset F in P(n). Finally, we obtain a number of results on the Ramsey properties of the random poset P(n,p).
ISSN:1042-9832
1098-2418
1098-2418
DOI:10.1002/rsa.20952