PreprintCC BY 4.0arXiv
Caterpillar trees are asymmetric, balanced trees are symmetric
Abstract
Two conjectures of Allman, Long and Rhodes are proven. The ultrametric exchangeable model captures the symmetries in allele distributions of ultrametric mechanistic models of coalescence and substitution in mathematical phylogeny. The dimension of this model with respect to the species tree leaf count is shown to be greatest for caterpillar trees and least for balanced trees.
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BibTeX
@misc{leppala2026caterpillar,
title = {{Caterpillar trees are asymmetric, balanced trees are symmetric}},
author = {Kalle Leppälä},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27151},
eprint = {2610.27151},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27151},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Caterpillar trees are asymmetric, balanced trees are symmetric
AU - Kalle Leppälä
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27151
UR - https://arxiv.org/abs/2610.27151
AB - Two conjectures of Allman, Long and Rhodes are proven. The ultrametric exchangeable model captures the symmetries in allele distributions of ultrametric mechanistic models of coalescence and substitution in mathematical phylogeny. The dimension of this model with respect to the species tree leaf count is shown to be greatest for caterpillar trees and least for balanced trees.
ER -