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The Asymptotic Number of Planar, Slim, Semimodular Lattice Diagrams

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Abstract

A lattice L is slim if it is finite and the set of its join-irreducible elements contains no three-element antichain. We prove that there exists a positive constant C such that, up to similarity, the number of planar diagrams of slim semimodular lattices of size n is asymptotically C · 2n.

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Authors and Affiliations

  1. University of Szeged, Bolyai Institute, Szeged, Aradi vértanúk tere 1, 6720, Hungary

    Gábor Czédli

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  1. Gábor Czédli
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Correspondence to Gábor Czédli.

Additional information

This research was supported by the NFSR of Hungary (OTKA), grant numbers K77432 and K83219, and by TÁMOP-4.2.1/B-09/1/KONV-2010-0005

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Czédli, G. The Asymptotic Number of Planar, Slim, Semimodular Lattice Diagrams. Order 33, 231–237 (2016). https://doi.org/10.1007/s11083-015-9361-0

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  • DOI: https://doi.org/10.1007/s11083-015-9361-0

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