Transit Functions and Clustering Systems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916108632588288 |
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| author | Changat, Manoj Shanavas, Ameera Vaheeda Stadler, Peter F. |
| author_facet | Changat, Manoj Shanavas, Ameera Vaheeda Stadler, Peter F. |
| contents | Transit functions serve not only as abstractions of betweenness and convexity but are also closely connected with clustering systems. Here, we investigate the canonical transit functions of binary clustering systems inspired by pyramids, i.e., interval hypergraphs. We provide alternative characterizations of weak hierarchies, and describe union-closed binary clustering systems as a subclass of pyramids and weakly pyramidal clustering systems as an interesting generalization. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_15662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transit Functions and Clustering Systems Changat, Manoj Shanavas, Ameera Vaheeda Stadler, Peter F. Discrete Mathematics 52A01, 68R01 Transit functions serve not only as abstractions of betweenness and convexity but are also closely connected with clustering systems. Here, we investigate the canonical transit functions of binary clustering systems inspired by pyramids, i.e., interval hypergraphs. We provide alternative characterizations of weak hierarchies, and describe union-closed binary clustering systems as a subclass of pyramids and weakly pyramidal clustering systems as an interesting generalization. |
| title | Transit Functions and Clustering Systems |
| topic | Discrete Mathematics 52A01, 68R01 |
| url | https://arxiv.org/abs/2401.15662 |