Geodesic
On certain integral Schreier graphs of the symmetric group
The electronic journal of combinatorics, Tome 14 (2007)

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

Zbl EuDML
We compute the spectrum of the Schreier graph of the symmetric group $S_n$ corresponding to the Young subgroup $S_2\times S_{n-2}$ and the generating set consisting of initial reversals. In particular, we show that this spectrum is integral and for $n\geq 8$ consists precisely of the integers $\{0,1,\ldots,n\}$. A consequence is that the first positive eigenvalue of the Laplacian is always $1$ for this family of graphs.
DOI : 10.37236/961
Classification : 05C25, 05C50
Mots-clés : spectrum, eigenvalue, Laplacian 
Paul E. Gunnells; Richard A. Scott; Byron L. Walden. On certain integral Schreier graphs of the symmetric group. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/961
@article{10_37236_961,
     author = {Paul E. Gunnells and Richard A. Scott and Byron L. Walden},
     title = {On certain integral {Schreier} graphs of the symmetric group},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/961},
     zbl = {1123.05048},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/961/}
}
TY  - JOUR
AU  - Paul E. Gunnells
AU  - Richard A. Scott
AU  - Byron L. Walden
TI  - On certain integral Schreier graphs of the symmetric group
JO  - The electronic journal of combinatorics
PY  - 2007
VL  - 14
UR  - http://geodesic.mathdoc.fr/articles/10.37236/961/
DO  - 10.37236/961
ID  - 10_37236_961
ER  - 
%0 Journal Article
%A Paul E. Gunnells
%A Richard A. Scott
%A Byron L. Walden
%T On certain integral Schreier graphs of the symmetric group
%J The electronic journal of combinatorics
%D 2007
%V 14
%U http://geodesic.mathdoc.fr/articles/10.37236/961/
%R 10.37236/961
%F 10_37236_961

Cité par Sources :