Geodesic
On the number of invertible homogeneous structures
Diskretnaya Matematika, Tome 15 (2003) no. 2, pp. 123-127.

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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. 
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     title = {On the number of invertible homogeneous structures},
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I. V. Kucherenko. On the number of invertible homogeneous structures. Diskretnaya Matematika, Tome 15 (2003) no. 2, pp. 123-127. http://geodesic.mathdoc.fr/item/DM_2003_15_2_a9/

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