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Existence thresholds and Ramsey properties of random posets
Author(s) -
FalgasRavry Victor,
Markström Klas,
Treglown Andrew,
Zhao Yi
Publication year - 2020
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20952
Subject(s) - partially ordered set , mathematics , combinatorics , discrete mathematics , chain (unit) , set (abstract data type) , property (philosophy) , computer science , physics , philosophy , epistemology , astronomy , programming language
Let ( n ) denote the power set of [ n ], ordered by inclusion, and let ( n , p ) denote the random poset obtained from ( n ) by retaining each element from ( n ) independently at random with probability p and discarding it otherwise. Given any fixed poset F we determine the threshold for the property that ( n , p ) contains F as an induced subposet. We also asymptotically determine the number of copies of a fixed poset F in ( n ) . Finally, we obtain a number of results on the Ramsey properties of the random poset ( n , p ) .