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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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Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

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Authors and Affiliations

  1. Operation Research Laboratory and Mathematics of Decision, University Mouloud MAMMERI, Tizi Ouzou, Algeria

    DJamel Talem & Bachir Sadi

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  1. DJamel Talem
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  2. Bachir Sadi
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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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