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

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