, Volume 30, Issue 2, pp 557–572 | Cite as

Parametrized Arity Gap

  • Miguel Couceiro
  • Erkko LehtonenEmail author
  • Tamás Waldhauser


We propose a parametrized version of arity gap. The parametrized arity gap gap (f, ℓ) of a function \(f \colon A^n \to B\) measures the minimum decrease in the number of essential variables of f when ℓ consecutive identifications of pairs of essential variables are performed. We determine gap (f, ℓ) for an arbitrary function f and a nonnegative integer ℓ. We also propose other variants of arity gap and discuss further problems pertaining to the effect of identification of variables on the number of essential variables of functions.


Arity gap Parametrized arity gap Essential variable Simple minor Variable identification minor 

Mathematics Subject Classifications (2010)

06A06 08A40 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Miguel Couceiro
    • 1
  • Erkko Lehtonen
    • 2
    Email author
  • Tamás Waldhauser
    • 1
    • 3
  1. 1.Mathematics Research UnitUniversity of LuxembourgLuxembourgLuxembourg
  2. 2.Computer Science and Communications Research UnitUniversity of LuxembourgLuxembourgLuxembourg
  3. 3.Bolyai InstituteUniversity of SzegedSzegedHungary

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