Existence thresholds and Ramsey properties of random posets

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

In: Random Structures and Algorithms, Vol. 57, No. 4, 12.2020, p. 1097-1133.

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Falgas-Ravry, Victor ; Markstrom, Klas ; Treglown, Andrew ; Zhao, Yi. / Existence thresholds and Ramsey properties of random posets. In: Random Structures and Algorithms. 2020 ; Vol. 57, No. 4. pp. 1097-1133.

Bibtex

@article{5e51293f60254180adc24234a170d864,
title = "Existence thresholds and Ramsey properties of random posets",
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).",
keywords = "boolean lattice, existence thresholds, Ramsey properties, random posets",
author = "Victor Falgas-Ravry and Klas Markstrom and Andrew Treglown and Yi Zhao",
year = "2020",
month = dec,
doi = "10.1002/rsa.20952",
language = "English",
volume = "57",
pages = "1097--1133",
journal = "Random Structures and Algorithms",
issn = "1042-9832",
publisher = "Wiley",
number = "4",

}

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 -