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arXiv · 0810.2279

On finite functions with non-trivial arity gap

Slavcho Shtrakov·Joerg Koppitz
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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 $2\leq gap(f)\leq n\leq k$. Our methods yield new combinatorial results about the number of such functions.

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Slavcho Shtrakov, Joerg Koppitz. 2010-03-05. On finite functions with non-trivial arity gap. https://arxiv.org/abs/0810.2279

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