Probability distributions on a linear vector space over a Galois field and on sets of permutations
Diskretnaya Matematika, Tome 9 (1997) no. 3, pp. 20-35
Voir la notice de l'article provenant de la source Math-Net.Ru
We give the exact and limit distributions of the number of vectors
from a union of subspaces of the $n$-dimensional vector
space $V_n$ over the Galois field $GF(q)$ which enter into a random set of
$d$, $1\le d\le n$, linearly independent vectors of this space. We prove
that the random
variable equal to the number of positions of a random
equiprobable permutation which are non-discordant to a
$d$-restriction of $m$ pairwise discordant permutations of degree
$n$ has in limit, as $n\to\infty$ and $m$ is fixed,
the Poisson distribution with parameter $m$. As a consequence we obtain
a simple proof of the asymptotic formula for the number of
$m\times n$ Latin rectangles where $m$ is fixed and $n\to\infty$.
@article{DM_1997_9_3_a1,
author = {V. N. Sachkov},
title = {Probability distributions on a linear vector space over a {Galois} field and on sets of permutations},
journal = {Diskretnaya Matematika},
pages = {20--35},
publisher = {mathdoc},
volume = {9},
number = {3},
year = {1997},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_1997_9_3_a1/}
}
V. N. Sachkov. Probability distributions on a linear vector space over a Galois field and on sets of permutations. Diskretnaya Matematika, Tome 9 (1997) no. 3, pp. 20-35. http://geodesic.mathdoc.fr/item/DM_1997_9_3_a1/