On Certain Integral Schreier Graphs of the Symmetric Group
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.
Keyword(s):
2019 ◽
Vol 18
(12)
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pp. 1950237
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2021 ◽
Vol 10
(6)
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pp. 2767-2784
2011 ◽
Vol 21
(01n02)
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pp. 147-178
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2014 ◽
Vol 24
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pp. 429-460
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