Geodesic
Finite Symmetric Functions with Non-Trivial Arity Gap
Serdica Journal of Computing, Tome 6 (2012) no. 4, pp. 419-436.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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 
@article{SJC_2012_6_4_a4,
     author = {Shtrakov, Slavcho and Koppitz, J\"org},
     title = {Finite {Symmetric} {Functions} with {Non-Trivial} {Arity} {Gap}},
     journal = {Serdica Journal of Computing},
     pages = {419--436},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJC_2012_6_4_a4/}
}
TY  - JOUR
AU  - Shtrakov, Slavcho
AU  - Koppitz, Jörg
TI  - Finite Symmetric Functions with Non-Trivial Arity Gap
JO  - Serdica Journal of Computing
PY  - 2012
SP  - 419
EP  - 436
VL  - 6
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJC_2012_6_4_a4/
LA  - en
ID  - SJC_2012_6_4_a4
ER  - 
%0 Journal Article
%A Shtrakov, Slavcho
%A Koppitz, Jörg
%T Finite Symmetric Functions with Non-Trivial Arity Gap
%J Serdica Journal of Computing
%D 2012
%P 419-436
%V 6
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJC_2012_6_4_a4/
%G en
%F SJC_2012_6_4_a4
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/