# Finite Symmetric Functions with Non-Trivial Arity Gap

Shtrakov, Slavcho; Koppitz, Jörg

Serdica Journal of Computing (2012)

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

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topShtrakov, 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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