Balanced pairs in partial orders
نویسنده
چکیده
An-balanced pair in a partially ordered set P = (X; <) is a pair (x; y) of elements of X such that the proportion of linear extensions of P with x below y lies between and 1 ?. The 1=3 ? 2=3 Conjecture states that, in every nite partial order P , not a chain, there is a 1 3-balanced pair. This was rst conjectured in a 1968 paper of Kislitsyn, and remains unsolved. We survey progress towards a resolution of the conjecture, and discuss some of the many related problems.
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عنوان ژورنال:
- Discrete Mathematics
دوره 201 شماره
صفحات -
تاریخ انتشار 1999