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Partial Orders on Weak Orders Convex Subsets

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Abstract

We study a visibility relation on the nonempty connected convex subsets of a finite partially ordered set and we investigate the partial orders representable as a visibility relation of such subsets of a weak order. Moreover, we consider restrictions where the subsets of the weak order are total orders or isomorphic total orders.

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References

  1. Faigle, U., Schrader, R. and Turán, G. (1992) The communication complexity of interval orders, Discrete Appl. Math. 40, 19–28.

    Google Scholar 

  2. Fishburn, P. C. (1985) Interval Orders and Interval Graphs: A Study of Partially Ordered Sets, Wiley, New York.

    Google Scholar 

  3. Gabow, H. N. (1981) A linear time recognition algorithm for interval dags, Inform. Process. Lett. 12, 20–22.

    Google Scholar 

  4. Garbe, R.: Algorithmic Aspects of Interval Orders, Ph.D. Thesis, University of Twente (The Netherlands), October 1994.

    Google Scholar 

  5. Kratsch, D. and Rampon, J.-X. (1998) Tree-visibility orders, Discrete Math. 190, 163–175.

    Google Scholar 

  6. Mitas, J. (1994) Minimal representation of semiorders with intervals of same length, in Proceedings of ORDAL'94, Lecture Notes in Comput. Sci. 831, Springer-Verlag, Berlin, pp. 162–175.

    Google Scholar 

  7. Müller, H. and Rampon, J.-X. (1997) Partial orders and their convex subsets, Discrete Math. 165/166, 507–517.

    Google Scholar 

  8. Reuter, K. (1991) The jump number and the lattice of maximal antichains, Discrete Math. 88, 289–307.

    Google Scholar 

  9. Scott, D. and Suppes, P. (1958) Foundational aspects of theories of measurement, J. Symbolic Logic 23, 113–128.

    Google Scholar 

  10. Trotter, W. T. (1992) Combinatorics and Partially Ordered Sets: Dimension Theory, The John Hopkins University Press, Baltimore, MD.

    Google Scholar 

  11. Wiener, N. (1914) A Contribution to the theory of relative position, Proc. Cambridge Philos. Soc. 17, 441–449.

    Google Scholar 

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Authors and Affiliations

  1. Institut für Informatik, FSU Jena, 07740, Jena, Germany

    Haiko Müller

  2. FST de l'Université de Nantes, 2 rue de la Houssinière, B.P. 92208, 44322, Nantes Cedex 3, France

    Jean-Xavier Rampon

Authors
  1. Haiko Müller
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  2. Jean-Xavier Rampon
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Müller, H., Rampon, JX. Partial Orders on Weak Orders Convex Subsets. Order 17, 103–123 (2000). https://doi.org/10.1023/A:1006497106096

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  • DOI: https://doi.org/10.1023/A:1006497106096

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