, Volume 32, Issue 2, pp 255–292 | Cite as

Hypomorphic Sperner Systems and Non-Reconstructible Functions

  • Miguel Couceiro
  • Erkko Lehtonen
  • Karsten Schölzel


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.


Reconstruction problem Sperner system Lattice term function Boolean function Clone 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Miguel Couceiro
    • 1
  • Erkko Lehtonen
    • 2
    • 3
    • 4
  • Karsten Schölzel
    • 5
  1. 1.LAMSADE–CNRSUniversité Paris-Dauphine, Place du Maréchal de Lattre de TassignyParis Cedex 16France
  2. 2.Computer Science and Communications Research UnitUniversity of LuxembourgLuxembourgLuxembourg
  3. 3.Centro de Álgebra da Universidade de LisboaLisbonPortugal
  4. 4.Departamento de Matemática, Faculdade de CiênciasUniversidade de LisboaLisbonPortugal
  5. 5.Mathematics Research UnitUniversity of LuxembourgLuxembourgLuxembourg

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