Diskretnaya Matematika, Tome 15 (2003) no. 2, pp. 123-127
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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/
@article{DM_2003_15_2_a9,
author = {I. V. Kucherenko},
title = {On the number of invertible homogeneous structures},
journal = {Diskretnaya Matematika},
pages = {123--127},
year = {2003},
volume = {15},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_2003_15_2_a9/}
}
TY - JOUR
AU - I. V. Kucherenko
TI - On the number of invertible homogeneous structures
JO - Diskretnaya Matematika
PY - 2003
SP - 123
EP - 127
VL - 15
IS - 2
UR - http://geodesic.mathdoc.fr/item/DM_2003_15_2_a9/
LA - ru
ID - DM_2003_15_2_a9
ER -
%0 Journal Article
%A I. V. Kucherenko
%T On the number of invertible homogeneous structures
%J Diskretnaya Matematika
%D 2003
%P 123-127
%V 15
%N 2
%U http://geodesic.mathdoc.fr/item/DM_2003_15_2_a9/
%G ru
%F DM_2003_15_2_a9
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.
