Transit Functions and Clustering Systems
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2024
- DOI:
- arXiv:
- arXiv:2401.15662
- Bibcode:
- 2024arXiv240115662C
- Keywords:
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- Computer Science - Discrete Mathematics;
- 52A01;
- 68R01
- E-Print:
- 27 pages, 8 figues, submitting to the journal Applicapable Analysis and Discrete Mathematics (AADM)