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Isolated Sublattices and Their Application to Counting Closure Operators

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Relational and Algebraic Methods in Computer Science (RAMiCS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13027))

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Abstract

This paper investigates the interplay between isolated sublattices and closure operators. Isolated sublattices are a special kind of sublattices which can serve to diminish the number of elements of a lattice by means of a quotient. At the same time, there are simple formulae for the relationship between the number of closure operators in the original lattice and the quotient lattice induced by isolated sublattices. This connection can be used to derive an algorithm for counting closure operators, provided the lattice contains suitable isolated sublattices.

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Acknowledgments

The author is grateful to every anonymous (especially the first) reviewer and to Bernhard Möller for valuable hints and remarks.

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Authors and Affiliations

  1. Deutsches Zentrum für Luft- und Raumfahrt, 86159, Augsburg, Germany

    Roland Glück

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  1. Roland Glück
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Correspondence to Roland Glück .

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Editors and Affiliations

  1. École polytechnique, Palaiseau, France

    Uli Fahrenberg

  2. Université Côte d’Azur, Nice, France

    Mai Gehrke

  3. Aix-Marseille University, Marseille, France

    Luigi Santocanale

  4. Brock University, St Catharines, ON, Canada

    Michael Winter

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Glück, R. (2021). Isolated Sublattices and Their Application to Counting Closure Operators. In: Fahrenberg, U., Gehrke, M., Santocanale, L., Winter, M. (eds) Relational and Algebraic Methods in Computer Science. RAMiCS 2021. Lecture Notes in Computer Science(), vol 13027. Springer, Cham. https://doi.org/10.1007/978-3-030-88701-8_12

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  • DOI: https://doi.org/10.1007/978-3-030-88701-8_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-88700-1

  • Online ISBN: 978-3-030-88701-8

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