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Linear extensions of finite posets

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arxiv 2311.02743 v2 pith:QCRYJORJ submitted 2023-11-05 math.CO cs.DM

Swee Hong Chan , Igor Pak This is my paper · ORCID
classification math.COcs.DM
keywords extensionsfiniteinequalitieslinearposetsresultsaspectsbounds
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We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the inequalities, and the computational complexity aspects of the results.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Equality conditions for correlation inequalities

    math.CO 2026-07 accept novelty 8.0 of 10

    Equality in the Ahlswede–Daykin and FKG inequalities holds if and only if the underlying lattice decomposes as a direct product and the functions cross-factor across the two components.

  2. Real-rootedness of rook-Eulerian polynomials

    math.CO 2025-02 conditional novelty 6.0 of 10

    Rook-Eulerian polynomials of Ferrers boards are real-rooted, with an interlacing refinement, and complete rook placements correspond to Bruhat lower intervals of 312-avoiding permutations.

  3. Graphical view on linear extensions of finite posets

    math.CO 2025-11 accept novelty 4.0 of 10

    A non-empty set of total orders is the set of linear extensions of some poset iff it is a geodesically convex set in the permutohedral graph; the paper gives an elementary proof and studies the graded lattice of such sets.

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