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Hypomorphic Sperner Systems and Non-Reconstructible Functions

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Abstract

A reconstruction problem is formulated for Sperner systems, and infinite families of non-reconstructible Sperner systems are presented. This has an application to a reconstruction problem for functions of several arguments and identification minors. Sperner systems being representations of certain monotone functions, infinite families of non-reconstructible functions are thus obtained. The clones of Boolean functions are completely classified in regard to reconstructibility.

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Authors and Affiliations

  1. LAMSADE–CNRS, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Miguel Couceiro

  2. Computer Science and Communications Research Unit, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, 1359, Luxembourg, Luxembourg

    Erkko Lehtonen

  3. Centro de Álgebra da Universidade de Lisboa, Avenida Professor Gama Pinto 2, 1649-003, Lisbon, Portugal

    Erkko Lehtonen

  4. Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, 1749-016, Lisbon, Portugal

    Erkko Lehtonen

  5. Mathematics Research Unit, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, 1359, Luxembourg, Luxembourg

    Karsten Schölzel

Authors
  1. Miguel Couceiro
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  2. Erkko Lehtonen
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  3. Karsten Schölzel
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Correspondence to Erkko Lehtonen.

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Couceiro, M., Lehtonen, E. & Schölzel, K. Hypomorphic Sperner Systems and Non-Reconstructible Functions. Order 32, 255–292 (2015). https://doi.org/10.1007/s11083-014-9330-z

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