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Semiorders and the 1/3–2/3 conjecture (1989)

Brightwell, Graham R.

Springer

Order 5 (1989), S. 369-380

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ISSN: 1572-9273

Keywords: 06A10 ; Poset ; linear extension ; semiorder ; 1/3–2/3 conjecture ; partially ordered set

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract A well-known conjecture of Fredman is that, for every finite partially ordered set (X, 〈) which is not a chain, there is a pair of elements x, y such that P(x〈y), the proportion of linear extensions of (X, 〈) with x below y, lies between 1/3 and 2/3. In this paper, we prove the conjecture in the special case when (X, 〈) is a semiorder. A property we call 2-separation appears to be crucial, and we classify all locally finite 2-separated posets of bounded width.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00353656

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