Elsevier

Discrete Mathematics

Volume 310, Issue 5, 6 March 2010, Pages 1016-1021
Discrete Mathematics

Average relational distance in linear extensions of posets

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Abstract

We consider a natural analogue of the graph linear arrangement problem for posets. Let P=(X,) be a poset that is not an antichain, and let λ:X[n] be an order-preserving bijection, that is, a linear extension of P. For any relation ab of P, the distance between a and b in λ is λ(b)λ(a). The average relational distance of λ, denoted distP(λ), is the average of these distances over all relations in P. We show that we can find a linear extension of P that maximises distP(λ) in polynomial time. Furthermore, we show that this maximum is at least 13(|X|+1), and this bound is extremal.

Keywords

Linear extensions of posets
Linear arrangement problem

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