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Abstract
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 language | English |
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Pages (from-to) | 1097-1133 |
Journal | Random Structures and Algorithms |
Volume | 57 |
Issue number | 4 |
Early online date | 6 Aug 2020 |
DOIs | |
Publication status | Published - Dec 2020 |
Keywords
- boolean lattice
- existence thresholds
- Ramsey properties
- random posets
ASJC Scopus subject areas
- Software
- Applied Mathematics
- General Mathematics
- Computer Graphics and Computer-Aided Design
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Dive into the research topics of 'Existence thresholds and Ramsey properties of random posets'. Together they form a unique fingerprint.Projects
- 1 Finished
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EPSRC Fellowship: Dr Andrew Treglown - Independence in groups, graphs and the integers
Treglown, A. (Principal Investigator)
Engineering & Physical Science Research Council
1/06/15 → 31/05/18
Project: Research Councils