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Maximizing a correlational ratio for linear extensions of posets

โœ Scribed by P. C. Fishburn

Publisher
Springer Netherlands
Year
1986
Tongue
English
Weight
308 KB
Volume
3
Category
Article
ISSN
0167-8094

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โœฆ Synopsis

Let p:P(12)/P( 12113), where P(tj) is the probability that i precedes j in a randomly chosen linear extension of a partially ordered set ({1,2 ..... n},<) in which points 1, 2 and 3 are mutually incomparable. A previous paper by the author (Order 1, 127 (1984)) proved that 13 <1. The present paper considers the maximization of p for each n/> 3. It shows that, with ~n = L(n + 3)/2J, the maximum P is at least Evidence that this value cannot be exceeded is given. It is also proved that the smallest possible value of P( 231)+P( 321) is 1/(~(n-nl ),2j) -AMS (MOS) subject classifications (1980).

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