The quantum Ramsey numbers $QR(2,k)$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916831342624768 |
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| author | Allen, Andrew Kornell, Andre |
| author_facet | Allen, Andrew Kornell, Andre |
| contents | Operator systems of matrices can be viewed as quantum analogues of finite graphs. This analogy suggests many natural combinatorial questions in linear algebra. We determine the quantum Ramsey numbers $QR(2,k)$ and the lower quantum Turán numbers $T^\downarrow(n, m)$ with $m \geq n/4$. In particular, we conclude that $QR(2,2) = 4$ and confirm Weaver's conjecture that $T^\downarrow(4, 1) = 4$. We also obtain a new result for the existence of anticliques in quantum graphs of low dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04128 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The quantum Ramsey numbers $QR(2,k)$ Allen, Andrew Kornell, Andre Operator Algebras Mathematical Physics Combinatorics Rings and Algebras Quantum Physics 46L89 (Primary) 05C55, 15A30, 46L07 (Secondary) Operator systems of matrices can be viewed as quantum analogues of finite graphs. This analogy suggests many natural combinatorial questions in linear algebra. We determine the quantum Ramsey numbers $QR(2,k)$ and the lower quantum Turán numbers $T^\downarrow(n, m)$ with $m \geq n/4$. In particular, we conclude that $QR(2,2) = 4$ and confirm Weaver's conjecture that $T^\downarrow(4, 1) = 4$. We also obtain a new result for the existence of anticliques in quantum graphs of low dimension. |
| title | The quantum Ramsey numbers $QR(2,k)$ |
| topic | Operator Algebras Mathematical Physics Combinatorics Rings and Algebras Quantum Physics 46L89 (Primary) 05C55, 15A30, 46L07 (Secondary) |
| url | https://arxiv.org/abs/2507.04128 |