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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1908.10327 |
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| _version_ | 1866912376943542272 |
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| author | Gollin, J. Pascal Kneip, Jay Lilian |
| author_facet | Gollin, J. Pascal Kneip, Jay Lilian |
| contents | Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.
First we characterise those tree sets that can be represented by tree sets arising from infinite trees; these are precisely those tree sets without a chain of order type ${ω+1}$. Then we introduce and study a topological generalisation of infinite trees which can have limit edges, and show that every infinite tree set can be represented by the tree set admitted by a suitable such tree-like space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_10327 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Representations of infinite tree-sets Gollin, J. Pascal Kneip, Jay Lilian Combinatorics 06-XX, 05C05, 05C83, 05C63 Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets. First we characterise those tree sets that can be represented by tree sets arising from infinite trees; these are precisely those tree sets without a chain of order type ${ω+1}$. Then we introduce and study a topological generalisation of infinite trees which can have limit edges, and show that every infinite tree set can be represented by the tree set admitted by a suitable such tree-like space. |
| title | Representations of infinite tree-sets |
| topic | Combinatorics 06-XX, 05C05, 05C83, 05C63 |
| url | https://arxiv.org/abs/1908.10327 |