3 research outputs found
The Reversal Ratio of a Poset
Felsner and Reuter introduced the linear extension diameter of a partially
ordered set , denoted \mbox{led}(\mathbf{P}), as the maximum
distance between two linear extensions of , where distance is
defined to be the number of incomparable pairs appearing in opposite orders
(reversed) in the linear extensions. In this paper, we introduce the reversal
ratio of as the ratio of the linear extension
diameter to the number of (unordered) incomparable pairs. We use probabilistic
techniques to provide a family of posets on at most
elements for which the reversal ratio , where
is a constant. We also examine the questions of bounding the reversal ratio
in terms of order dimension and width.Comment: 10 pages, 2 figures; Accepted for publication in ORDE