Geodesic
On a balanced property of derangements
The electronic journal of combinatorics, Tome 13 (2006)

Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website

Zbl arXiv EuDML
We prove an interesting fact describing the location of the roots of the generating polynomials of the numbers of derangements of length $n$, counted by their number of cycles. We then use this result to prove that if $k$ is the number of cycles of a randomly selected derangement of length $n$, then the probability that $k$ is congruent to a given $r$ modulo a given $q$ converges to $1/q$. Finally, we generalize our results to $a$-derangements, which are permutations in which each cycle is longer than $a$.
DOI : 10.37236/1128
Classification : 05A16
Mots-clés : generating polynomials, number of cycles 
Miklós Bóna. On a balanced property of derangements. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1128
@article{10_37236_1128,
     author = {Mikl\'os B\'ona},
     title = {On a balanced property of derangements},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1128},
     zbl = {1112.05008},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1128/}
}
TY  - JOUR
AU  - Miklós Bóna
TI  - On a balanced property of derangements
JO  - The electronic journal of combinatorics
PY  - 2006
VL  - 13
UR  - http://geodesic.mathdoc.fr/articles/10.37236/1128/
DO  - 10.37236/1128
ID  - 10_37236_1128
ER  - 
%0 Journal Article
%A Miklós Bóna
%T On a balanced property of derangements
%J The electronic journal of combinatorics
%D 2006
%V 13
%U http://geodesic.mathdoc.fr/articles/10.37236/1128/
%R 10.37236/1128
%F 10_37236_1128

Cité par Sources :