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Subdiagrams equal in number to their duals

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Abstract

In the middle 1930's, the early days of combinatorial lattice theory, it had been conjectured thatin any finite modular lattice the number of join-irreducible elements equals the number of meetirreducible elements. The conjecture was settled in 1954 by R. P. Dilworth in a remarkable combinatorial generalization. Quite recently we have been led to this question. Which ordered setsS satisfy the property that,for any modular lattice M, the number of subdiagrams of M isomorphic to S equals the number of subdiagrams of M dually isomorphic to S?

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References

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Authors and Affiliations

  1. FB4 Technische Hochschule Darmstadt, AGI, D-6100, Darmstadt, Federal Republic of Germany

    Klaus Reuter & Ivan Rival

  2. Department of Computer Science, University of Ottawa, K1N 9B4, Ottawa, Canada

    Klaus Reuter & Ivan Rival

Authors
  1. Klaus Reuter
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  2. Ivan Rival
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To the memory of András Huhn

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Reuter, K., Rival, I. Subdiagrams equal in number to their duals. Algebra Universalis 23, 70–76 (1986). https://doi.org/10.1007/BF01190913

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  • DOI: https://doi.org/10.1007/BF01190913

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