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Invariant Computation in a Poset

Convergence to a Chain

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Abstract

Kong and Ribemboim (1994) define for every poset P a sequence P = D0(P), D(P), D2(P), D3(P)… of posets, where Di(P) = D(Di− 1(P)) consists of all maximal antichains of Di− 1(P). They prove that for a finite poset P, there exists an integer i ≥ 0 such that Di(P) is a chain. In this paper, for every finite poset P, we show how to calculate the smallest integer i for which Di(P) is a chain.

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References

  1. Caspard, N., Leclerc, B., Monjardet, B.: Finite Ordered Sets: Concepts, Results and Uses. Springer, New York (2007)

    MATH  Google Scholar 

  2. Habib, M.: Comparability invariants. Ann. Discrete Math. 23, 371–386 (1984)

    MathSciNet  MATH  Google Scholar 

  3. Kelly, D.: Invariants of finite comparability graphs. Order 3, 155–158 (1986)

    Article  MathSciNet  Google Scholar 

  4. Kong, T.Y., Ribemboim, P.: Chaining of Partially Ordered Sets. C. R. Acad. Sci. Paris, t. 319, Série I 533–537 (1994)

  5. Sadi, B.: Suite d’Ensembles Partiellement Ordonnés. Arima 4, 66–71 (2006)

    Google Scholar 

  6. Schröder, B.: Ordered Sets, 2nd edn. Springer, New York (2016)

    MATH  Google Scholar 

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Correspondence to DJamel Talem.

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Talem, D., Sadi, B. Invariant Computation in a Poset. Order 39, 1–6 (2022). https://doi.org/10.1007/s11083-021-09559-2

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  • DOI: https://doi.org/10.1007/s11083-021-09559-2

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