, Volume 27, Issue 3, pp 261–282 | Cite as

Join-Irreducible Boolean Functions



This paper is a contribution to the study of a quasi-order on the set Ω of Boolean functions, the simple minor quasi-order. We look at the join-irreducible members of the resulting poset \(\tilde{\Omega}\). Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial property of hypergraphs. We observe that among Steiner systems, those which yield join-irreducible members of \(\tilde{\Omega}\) are the − 2-monomorphic Steiner systems. We also describe the graphs which correspond to join-irreducible members of \(\tilde{\Omega}\).


Boolean function Minor quasi-order Hypergraph Designs Steiner systems Monomorphy 

Mathematics Subject Classifications (2010)

05C75 05C65 05B05 05B07 06A07 06E30 94C10 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Moncef Bouaziz
    • 1
  • Miguel Couceiro
    • 2
  • Maurice Pouzet
    • 3
    • 4
  1. 1.Institut Supérieur des Technologies Médicales de TunisTunisTunisie
  2. 2.Mathematics Research UnitUniversity of LuxembourgLuxembourgLuxembourg
  3. 3.ICJ, Department of MathematicsUniversité Claude-Bernard Lyon1Villeurbanne CedexFrance
  4. 4.Department of Mathematics and StatisticsThe University of CalgaryCalgaryCanada

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