Existence thresholds and Ramsey properties of random posets

Victor Falgas-Ravry; Klas Markstrom; Andrew Treglown; Yi Zhao

doi:10.1002/rsa.20952

Existence thresholds and Ramsey properties of random posets

Victor Falgas-Ravry, Klas Markstrom, Andrew Treglown, Yi Zhao

Mathematics

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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
Pages (from-to)	1097-1133
Journal	Random Structures and Algorithms
Volume	57
Issue number	4
Early online date	6 Aug 2020
DOIs	https://doi.org/10.1002/rsa.20952
Publication status	Published - Dec 2020

Keywords

boolean lattice
existence thresholds
Ramsey properties
random posets

ASJC Scopus subject areas

Software
Applied Mathematics
Mathematics(all)
Computer Graphics and Computer-Aided Design

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10.1002/rsa.20952Licence: None: All rights reserved

FalgasRavryV2020Existence
This is the peer reviewed version of the following article: algas‐Ravry, V, Markström, K, Treglown, A, Zhao, Y. Existence thresholds and Ramsey properties of random posets. Random Struct Alg. 2020, which has been published in final form at: https://doi.org/10.1002/rsa.20952. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
Accepted author manuscript, 527 KBLicence: Other (please specify with Rights Statement)

https://doi.org/10.1002/rsa.20952Licence: None: All rights reserved

EPSRC Fellowship: Dr Andrew Treglown - Independence in groups, graphs and the integers
Treglown, A.
Engineering & Physical Science Research Council
1/06/15 → 31/05/18
Project: Research Councils

Cite this

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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).",

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AU - Treglown, Andrew

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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

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SN - 1042-9832

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EP - 1133

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 4

ER -

Existence thresholds and Ramsey properties of random posets

Abstract

Keywords

ASJC Scopus subject areas

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Projects

EPSRC Fellowship: Dr Andrew Treglown - Independence in groups, graphs and the integers

Cite this