Higher-rank trees arising from polyhedral graphs
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914620980068352 |
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| author | Pask, David |
| author_facet | Pask, David |
| contents | We introduce a new family of higher-rank graphs, whose construction was inspired by the graphical techniques of Lambek \cite{Lambek} and Johnstone \cite{Johnstone} used for monoid and category emedding results. We show that they are planar $k$-trees for $2 \le k \le 4$. We also show that higher-rank trees differ from $1$-trees by giving examples of higher-rank trees having properties which are impossible for $1$-trees. Finally, we collect more examples of higher-rank planar trees which are not in our family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher-rank trees arising from polyhedral graphs Pask, David Combinatorics Category Theory Operator Algebras 05C20 (Primary) 57M50, 18D99 (Secondary) We introduce a new family of higher-rank graphs, whose construction was inspired by the graphical techniques of Lambek \cite{Lambek} and Johnstone \cite{Johnstone} used for monoid and category emedding results. We show that they are planar $k$-trees for $2 \le k \le 4$. We also show that higher-rank trees differ from $1$-trees by giving examples of higher-rank trees having properties which are impossible for $1$-trees. Finally, we collect more examples of higher-rank planar trees which are not in our family. |
| title | Higher-rank trees arising from polyhedral graphs |
| topic | Combinatorics Category Theory Operator Algebras 05C20 (Primary) 57M50, 18D99 (Secondary) |
| url | https://arxiv.org/abs/2407.14048 |