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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.02825 |
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| _version_ | 1866913519045181440 |
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| author | Gao, Su Wang, Ruijun Wang, Tianhao |
| author_facet | Gao, Su Wang, Ruijun Wang, Tianhao |
| contents | We prove that for any generating set $S$ of $\mathbb {Z}^n$, the continuous edge chromatic number of the Schreier graph of the Bernoulli shift action $G=F(S,2^{\mathbb{Z}^n})$ is $χ'_c(G)=χ'(G)+1$. In particular, for the standard generating set, the continuous edge chromatic number of $F(2^{\mathbb {Z}^n})$ is $2n+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02825 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Continuous Edge Chromatic Numbers of Abelian Group Actions Gao, Su Wang, Ruijun Wang, Tianhao Combinatorics Logic 03E15 We prove that for any generating set $S$ of $\mathbb {Z}^n$, the continuous edge chromatic number of the Schreier graph of the Bernoulli shift action $G=F(S,2^{\mathbb{Z}^n})$ is $χ'_c(G)=χ'(G)+1$. In particular, for the standard generating set, the continuous edge chromatic number of $F(2^{\mathbb {Z}^n})$ is $2n+1$. |
| title | Continuous Edge Chromatic Numbers of Abelian Group Actions |
| topic | Combinatorics Logic 03E15 |
| url | https://arxiv.org/abs/2406.02825 |