Existence thresholds and Ramsey properties of random posets

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Colleges, School and Institutes

External organisations

  • Georgia State University
  • Umea Univ


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 ran-dom with probability p and discarding it otherwise. Given anyfixed poset F we determine the threshold for the property that P(n, p) contains F as an induced subposet. We also asymptot-ically determine the number of copies of a fixed poset F in P(n). Finally, we obtain a number of results on the Ramseyproperties of the random poset P(n, p).


Original languageEnglish
Pages (from-to)1097-1133
JournalRandom Structures and Algorithms
Issue number4
Early online date6 Aug 2020
Publication statusPublished - Dec 2020


  • boolean lattice, existence thresholds, Ramsey properties, random posets