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Linear Extensions and Comparable Pairs in Partial Orders

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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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Acknowledgements

We are grateful to the referees, whose comments have led to a much improved paper, and have encouraged us for example to make explicit the Conjectures 12 and 13.

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Authors and Affiliations

  1. Department of Statistics, University of Oxford, Oxford, UK

    Colin McDiarmid

  2. Department of Mathematical Sciences, University of Essex, Colchester, UK

    David Penman & Vasileios Iliopoulos

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  1. Colin McDiarmid
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  2. David Penman
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  3. Vasileios Iliopoulos
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Correspondence to Colin McDiarmid.

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McDiarmid, C., Penman, D. & Iliopoulos, V. Linear Extensions and Comparable Pairs in Partial Orders. Order 35, 403–420 (2018). https://doi.org/10.1007/s11083-017-9439-y

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  • DOI: https://doi.org/10.1007/s11083-017-9439-y

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