# Existence thresholds and Ramsey properties of random posets

Research output: Contribution to journal › Article › peer-review

## Standard

**Existence thresholds and Ramsey properties of random posets.** / Falgas-Ravry, Victor; Markstrom, Klas; Treglown, Andrew; Zhao, Yi.

Research output: Contribution to journal › Article › peer-review

## Harvard

*Random Structures and Algorithms*, vol. 57, no. 4, pp. 1097-1133. https://doi.org/10.1002/rsa.20952

## APA

*Random Structures and Algorithms*,

*57*(4), 1097-1133. https://doi.org/10.1002/rsa.20952

## Vancouver

## Author

## Bibtex

}

## RIS

TY - JOUR

T1 - Existence thresholds and Ramsey properties of random posets

AU - Falgas-Ravry, Victor

AU - Markstrom, Klas

AU - Treglown, Andrew

AU - Zhao, Yi

PY - 2020/12

Y1 - 2020/12

N2 - 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).

AB - 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).

KW - boolean lattice

KW - existence thresholds

KW - Ramsey properties

KW - random posets

UR - https://onlinelibrary.wiley.com/journal/10982418

UR - http://www.scopus.com/inward/record.url?scp=85089101684&partnerID=8YFLogxK

U2 - 10.1002/rsa.20952

DO - 10.1002/rsa.20952

M3 - Article

VL - 57

SP - 1097

EP - 1133

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

SN - 1042-9832

IS - 4

ER -