# Finite Symmetric Functions with Non-Trivial Arity Gap

• Volume: 6, Issue: 4, page 419-436
• ISSN: 1312-6555

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## Abstract

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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.

## How to cite

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Shtrakov, Slavcho, and Koppitz, Jörg. "Finite Symmetric Functions with Non-Trivial Arity Gap." Serdica Journal of Computing 6.4 (2012): 419-436. <http://eudml.org/doc/250936>.

@article{Shtrakov2012,
abstract = {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.},
author = {Shtrakov, Slavcho, Koppitz, Jörg},
journal = {Serdica Journal of Computing},
keywords = {Symmetric Function; Essential Variable; Subfunction; Identification Minor; Essential Arity Gap; Gap Index; Separable Set; symmetric function; essential variable; subfunction; identification minor; essential arity gap; gap index; separable set},
language = {eng},
number = {4},
pages = {419-436},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Finite Symmetric Functions with Non-Trivial Arity Gap},
url = {http://eudml.org/doc/250936},
volume = {6},
year = {2012},
}

TY - JOUR
AU - Shtrakov, Slavcho
AU - Koppitz, Jörg
TI - Finite Symmetric Functions with Non-Trivial Arity Gap
JO - Serdica Journal of Computing
PY - 2012
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 6
IS - 4
SP - 419
EP - 436
AB - 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.
LA - eng
KW - Symmetric Function; Essential Variable; Subfunction; Identification Minor; Essential Arity Gap; Gap Index; Separable Set; symmetric function; essential variable; subfunction; identification minor; essential arity gap; gap index; separable set
UR - http://eudml.org/doc/250936
ER -

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