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arXiv · 1603.02901

Linear Extensions and Comparable Pairs in Partial Orders

Colin McDiarmid·David Penman·Vasileios Iliopoulos
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Abstract

We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on $n$ elements, which has close to a third of the pairs comparable with high probability: we show that the number of linear extensions is $n! \, 2^{-Θ(n)}$ with high probability.

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Colin McDiarmid, David Penman, Vasileios Iliopoulos. 2018-10-15. Linear Extensions and Comparable Pairs in Partial Orders. https://doi.org/10.1007/s11083-017-9439-y

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