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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.00410 |
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Table of Contents:
- A Transposition graph $T_n$ is defined as a Cayley graph over the symmetric group $Sym_n$ generated by all transpositions. It is known that the spectrum of $T_n$ consists of integers, but it is not known exactly how these numbers are distributed. In this paper we prove that integers from the segment $[-n, n]$ lie in the spectrum of $T_n$ for any $n\geqslant 31$. Using this fact we also prove the main result of this paper that a segment of quadratic length with respect to $n$ lies in the spectrum of $T_n$.