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A note on the dimension of a poset

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Abstract

It is shown that the dimension of a poset is the smallest cardinal number λ such that there is an embedding of the poset into a strict product of λ linear orders.

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References

  1. HiraguchiTosio (1951) On the dimension of partially ordered sets, Sci. Rep. Kanazawa Univ. 1, 77–94. MR 17, p. 19.

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  2. DushnikB. & MillerE. W. (1941) Partially ordered sets, Amer. J. Math. 63, 600–610. MR 12 # 470.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, T2N 1N4, Alberta, Canada

    E. C. Milner

  2. Department of Mathematics, University of Lyon I, Villeurbanne, France

    M. Pouzet

Authors
  1. E. C. Milner
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  2. M. Pouzet
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Communicated by D. Kelly

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Milner, E.C., Pouzet, M. A note on the dimension of a poset. Order 7, 101–102 (1990). https://doi.org/10.1007/BF00383178

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  • DOI: https://doi.org/10.1007/BF00383178

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