On finite functions with non-trivial arity gap

Abstract

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 $f$. We particularly solve a problem concerning the explicit determination of $n$-ary $k-$valued functions $f$ with $2\le gap(f)\le n\le k$. Our methods yield new combinatorial results about the number of such functions.

17 pages, Int. Conf. Algebraic and Combinatorial Coding Theory, ACCT2008, June 16 - Sunday 22, 2008, Pamporovo, BULGARIA

References in corpus (4)

• Generalizations of Swierczkowski's lemma and the arity gap of finite functions
• Essential Variables and Separable Sets in Universal Algebra
• Essential arity gap of Boolean functions
• Tree Automata and Essential Input Variables

Cited by in corpus (1)

• Decompositions of functions based on arity gap