Conjugation of reddening sequences and conjugation difference
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915223545315328 |
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| author | Liu, Siyang Pan, Jie |
| author_facet | Liu, Siyang Pan, Jie |
| contents | We describe the conjugation of the reddening sequence according to the formula of $c$-vectors with respect to changing the initial seed. As applications, we extend the Rotation Lemma, the Target before Source Theorem, and the mutation invariant property of the existence of reddening sequences to totally sign-skew-symmetric cluster algebras. Furthermore, this also leads to the construction of conjugation difference which characterizes the number of red mutations a maximal green sequence should admit in any matrix pattern with the initial seed changed via mutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09585 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conjugation of reddening sequences and conjugation difference Liu, Siyang Pan, Jie Combinatorics 13F60 We describe the conjugation of the reddening sequence according to the formula of $c$-vectors with respect to changing the initial seed. As applications, we extend the Rotation Lemma, the Target before Source Theorem, and the mutation invariant property of the existence of reddening sequences to totally sign-skew-symmetric cluster algebras. Furthermore, this also leads to the construction of conjugation difference which characterizes the number of red mutations a maximal green sequence should admit in any matrix pattern with the initial seed changed via mutations. |
| title | Conjugation of reddening sequences and conjugation difference |
| topic | Combinatorics 13F60 |
| url | https://arxiv.org/abs/2410.09585 |