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Minor Posets of Functions as Quotients of Partition Lattices

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Abstract

We study the structure of the partially ordered set of minors of an arbitrary function of several variables. We give an abstract characterization of such “minor posets” in terms of colorings of partition lattices, and we also present infinite families of examples as well as some constructions that can be used to build new minor posets.

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Acknowledgements

Research supported by the Hungarian National Research, Development and Innovation Office (NKFIH grants no. K104251 and K115518) and by the János Bolyai Research Scholarship. This work was developed during the authors’ mutual visits to the Technische Universität Dresden and the University of Szeged. The authors would like to thank the anonymous reviewers for their valuable comments and suggestions for improving the paper.

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Authors and Affiliations

  1. Technische Universität Dresden, Institut für Algebra, 01062, Dresden, Germany

    Erkko Lehtonen

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

    Tamás Waldhauser

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  1. Erkko Lehtonen
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  2. Tamás Waldhauser
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Correspondence to Tamás Waldhauser.

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Lehtonen, E., Waldhauser, T. Minor Posets of Functions as Quotients of Partition Lattices. Order 36, 23–41 (2019). https://doi.org/10.1007/s11083-018-9453-8

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  • DOI: https://doi.org/10.1007/s11083-018-9453-8

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