Geodesic
On finite functions with non-trivial arity gap
Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 2, pp. 217-245

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Given an n-ary k-valued function f, gap(f) denotes the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f.
Keywords: essential variable, identification minor, essential arity gap 
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Shtrakov, Slavcho; Koppitz, Jörg. On finite functions with non-trivial arity gap. Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 2, pp. 217-245. http://geodesic.mathdoc.fr/item/DMGAA_2010_30_2_a5/