Geodesic
Finite Symmetric Functions with Non-Trivial Arity Gap
Serdica Journal of Computing, Tome 6 (2012) no. 4, pp. 419-436 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

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Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. In the present paper we study the properties of the symmetric function with non-trivial arity gap (2 ≤ gap(f)). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of essential variables in symmetric functions with non-trivial arity gap are separable. ACM Computing Classification System (1998): G.2.0.
Keywords: Symmetric Function, Essential Variable, Subfunction, Identification Minor, Essential Arity Gap, Gap Index, Separable Set 
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Shtrakov, Slavcho; Koppitz, Jörg. Finite Symmetric Functions with Non-Trivial Arity Gap. Serdica Journal of Computing, Tome 6 (2012) no. 4, pp. 419-436. http://geodesic.mathdoc.fr/item/SJC_2012_6_4_a4/