Brightwell, Graham and Keller, Mitchel T.
(2015)
The reversal ratio of a poset.
Order  a Journal on the Theory of Ordered Sets and Its Applications, 32 (1).
pp. 4352.
ISSN 01678094
Abstract
Felsner and Reuter introduced the linear extension diameter of a partially ordered set P, denoted led(P), as the maximum distance between two linear extensions of P, 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 RR(P) of P 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 P k on at most k log k elements for which the reversal ratio RR(P k ) ≤ C / log k, where C is an absolute constant. We also examine the questions of bounding the reversal ratio in terms of order dimension and width.
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