Modelirovanie i analiz informacionnyh sistem, Tome 14 (2007) no. 4, pp. 53-56
Citer cet article
G. R. Chelnokov. On the lower estimate for $k+1$-nondecomposible permutations. Modelirovanie i analiz informacionnyh sistem, Tome 14 (2007) no. 4, pp. 53-56. http://geodesic.mathdoc.fr/item/MAIS_2007_14_4_a8/
@article{MAIS_2007_14_4_a8,
author = {G. R. Chelnokov},
title = {On the lower estimate for $k+1$-nondecomposible permutations},
journal = {Modelirovanie i analiz informacionnyh sistem},
pages = {53--56},
year = {2007},
volume = {14},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MAIS_2007_14_4_a8/}
}
TY - JOUR
AU - G. R. Chelnokov
TI - On the lower estimate for $k+1$-nondecomposible permutations
JO - Modelirovanie i analiz informacionnyh sistem
PY - 2007
SP - 53
EP - 56
VL - 14
IS - 4
UR - http://geodesic.mathdoc.fr/item/MAIS_2007_14_4_a8/
LA - ru
ID - MAIS_2007_14_4_a8
ER -
%0 Journal Article
%A G. R. Chelnokov
%T On the lower estimate for $k+1$-nondecomposible permutations
%J Modelirovanie i analiz informacionnyh sistem
%D 2007
%P 53-56
%V 14
%N 4
%U http://geodesic.mathdoc.fr/item/MAIS_2007_14_4_a8/
%G ru
%F MAIS_2007_14_4_a8
A permutation $\tau$ is called $k+1$-nondecomposible if the following condition holds: if $\{a_1,\dots,a_in\}$ is a set of natural numbers such that $1\le a_1,\dots,$ and $\tau(a_1)\tau(a_2)\dots\tau(a_i)$, then $i\le k$. By $f(n,k)$ denote the number of all not $k+1$-nondecomposible permutations. The following statement was proved in this paper: suppose $K(n)=o(\root3\of{n}/\ln n)$; then $f(n,k)=k^{2n-o(n)}$ for every $k \le K(n)$.
