On finite functions with non-trivial arity gap

Details On finite functions with non-trivial arity gap On finite functions with non-trivial arity gap

2008-10-13

arxiv.org/abs/0810.2279v6

Computer Science

Discrete Mathematics

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

Scientific paper

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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