Transit Functions and PyramidLike Binary Clustering Systems
Abstract
Binary clustering systems are closely related to monotone transit functions. An interesting class are pyramidal transit functions defined by the fact that their transit sets form an interval hypergraph. We investigate here properties of transit function $R$, such as unionclosure, that are sufficient to ensure that $R$ is at least weakly pyramidal. Necessary conditions for pyramidal transit functions are derived from the five forbidden configurations in Tucker's characterization of interval hypergraphs. The first corresponds to $\beta$acyclicity, also known as total balancedness, for which we obtain three alternative characterizations. For monotonous transit functions, the last forbidden configuration becomes redundant, leaving us with characterization of pyramidal transit functions in terms of four additional conditions.
 Publication:

arXiv eprints
 Pub Date:
 December 2022
 DOI:
 10.48550/arXiv.2212.08721
 arXiv:
 arXiv:2212.08721
 Bibcode:
 2022arXiv221208721C
 Keywords:

 Mathematics  Combinatorics