Transit Functions and Clustering Systems
Discrete Mathematics
2024-01-30 v1
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.
Keywords
Cite
@article{arxiv.2401.15662,
title = {Transit Functions and Clustering Systems},
author = {Manoj Changat and Ameera Vaheeda Shanavas and Peter F. Stadler},
journal= {arXiv preprint arXiv:2401.15662},
year = {2024}
}
Comments
27 pages, 8 figues, submitting to the journal Applicapable Analysis and Discrete Mathematics (AADM)