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Generating boxes from ordered sets and graphs

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Abstract

LetE be a set and letL be a family of subsets ofE. A subsets ofE is called atransversal ofL ifs intersects each member ofL in exactly one element, that is |s∩l|=1, for everyl inL. We denoteT(L) the set of all transversals ofL. A pairB=(L, C) of families of subsets ofE is abox onE if it satisfies the following conditions:

  1. (i)

    ∪L=∪C=E, that is bothL andC coverE.

  2. (ii)

    T(L)=C andT(C)=L.

Boxes have been introduced by Boë [2]. Our aim in this paper is to study particular boxes, using techniques of ordered sets and graphs.

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References

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Authors and Affiliations

  1. Department of Mathematics, University Claude Bernard, 43 Boulevard 11 Novembre 1918, 69622, Villeurbanne, France

    Maurice Pouzet

  2. Department of Mathematics and Statistics, The University of Calgary, 2500 University Dr. NW, T2N 1N4, Calgary, Alberta, Canada

    Robert Woodrow

  3. Department of Computer Science, University of Ottawa, 34 George Glinski, K1N 6N5, Ottawa, Ontario, Canada

    Nejib Zaguia

Authors
  1. Maurice Pouzet
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  2. Robert Woodrow
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  3. Nejib Zaguia
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Additional information

Communicated by I. Rival

Research supported by NATO Grant 339-85, PRC Math. Info. and NSERC Canada.

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Pouzet, M., Woodrow, R. & Zaguia, N. Generating boxes from ordered sets and graphs. Order 9, 111–126 (1992). https://doi.org/10.1007/BF00814404

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  • DOI: https://doi.org/10.1007/BF00814404

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