On the number of invertible homogeneous structures

I. V. Kucherenko

Diskretnaya Matematika, Tome 15 (2003) no. 2, pp. 123-127

Résumé

We estimate the number $r(n,m)$ of functions of $n$-valued logic in $m+1$ variables which are local transition functions of reversible homogeneous structures with arbitrary fixed neighbourhood pattern consisting of $m$ vectors. It follows from the results obtained in the paper that if $n\to\infty$, then $$ \ln r(n,m)\sim n^{m+1}\ln n $$ uniformly in $m$. This research was supported by the Russian Foundation for Basic Research, grant 02–01–00162.