Proof of a conjecture on eigenvalues of transposition graph
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911009528086528 |
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| author | Ku, Cheng Yeaw Xu, Leyou |
| author_facet | Ku, Cheng Yeaw Xu, Leyou |
| contents | The transposition graph $Cay(S_n,T_n)$ is the Cayley graph on the symmetric group $S_n$ generated by the set $T_n$ of all transpositions. In this paper, we show that each integer in the interval $\left[-{\lfloor(2n+1)/3 \rfloor\choose 2}, {\lfloor(2n+1)/3 \rfloor\choose 2}\right]$ is an eigenvalue of $Cay(S_n,T_n)$. This proves a recent conjecture by Kravchuk \cite{Kravchuk}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14419 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proof of a conjecture on eigenvalues of transposition graph Ku, Cheng Yeaw Xu, Leyou Combinatorics The transposition graph $Cay(S_n,T_n)$ is the Cayley graph on the symmetric group $S_n$ generated by the set $T_n$ of all transpositions. In this paper, we show that each integer in the interval $\left[-{\lfloor(2n+1)/3 \rfloor\choose 2}, {\lfloor(2n+1)/3 \rfloor\choose 2}\right]$ is an eigenvalue of $Cay(S_n,T_n)$. This proves a recent conjecture by Kravchuk \cite{Kravchuk}. |
| title | Proof of a conjecture on eigenvalues of transposition graph |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.14419 |