Proportional transitivity in linear extensions of ordered sets
β Scribed by P.C Fishburn
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 457 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let P be an ordered set. P is said to have the finite cutset property if for every x in P there is a finite set F of elements which are noncomparable to x such that every maximal chain in P meets {x} t.J F. It is well known that this property is equivalent to the space of maximal chains of P being c
A popular model of random orders is obtained by taking two disjoint n-element antichains A, and Al, and putting in each relation in A, x A, with probability l/2, all the choices being made independently. We estimate the number of linear extensions of such an ordered set, showing that this number is
It is well known that the linear extension majority relation of a partially ordered set (P, β€ P ) can contain cycles when at least 9 elements are present in P. Computer experiments have uncovered all posets with 9 elements containing such cycles and limited frequency estimates for linear extension m