The miracle of integer eigenvalues
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866911797189017600 |
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| author | Kenyon, Richard Kontsevich, Maxim Ogievetsky, Oleg Pohoata, Cosmin Sawin, Will Shlosman, Senya |
| author_facet | Kenyon, Richard Kontsevich, Maxim Ogievetsky, Oleg Pohoata, Cosmin Sawin, Will Shlosman, Senya |
| contents | For partially ordered sets $X$ we consider the square matrices $M^{X}$ with rows and columns indexed by linear extensions of the partial order on $X$. Each entry $\left( M^{X}\right)_{PQ}$ is a formal variable defined by a pedestal of the linear order $Q$ with respect to linear order $P$. We show that all the eigenvalues of any such matrix $M^{X}$ are $\mathbb{Z}$-linear combinations of those variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05291 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The miracle of integer eigenvalues Kenyon, Richard Kontsevich, Maxim Ogievetsky, Oleg Pohoata, Cosmin Sawin, Will Shlosman, Senya Combinatorics Mathematical Physics For partially ordered sets $X$ we consider the square matrices $M^{X}$ with rows and columns indexed by linear extensions of the partial order on $X$. Each entry $\left( M^{X}\right)_{PQ}$ is a formal variable defined by a pedestal of the linear order $Q$ with respect to linear order $P$. We show that all the eigenvalues of any such matrix $M^{X}$ are $\mathbb{Z}$-linear combinations of those variables. |
| title | The miracle of integer eigenvalues |
| topic | Combinatorics Mathematical Physics |
| url | https://arxiv.org/abs/2401.05291 |