# Galois connections for phylogenetic networks and their polytopes

@article{Forcey2020GaloisCF, title={Galois connections for phylogenetic networks and their polytopes}, author={Stefan Forcey and Drew Scalzo}, journal={arXiv: Combinatorics}, year={2020} }

We describe Galois connections which arise between two kinds of combinatorial structures, both of which generalize trees with labelled leaves, and then apply those connections to a family of polytopes.
The graphs we study can be imbued with metric properties or associated to vectors. Famous examples are the Billera-Holmes-Vogtmann metric space of phylogenetic trees, and the Balanced Minimal Evolution polytopes of phylogenetic trees described by Eickmeyer, Huggins, Pachter and Yoshida. Recently… Expand

#### 2 Citations

Circular planar electrical networks, Split systems, and Phylogenetic networks

- Mathematics
- 2021

We study a new invariant of circular planar electrical networks, well known to phylogeneticists: the circular split system. We use our invariant to answer some open questions about levels of… Expand

Phylogenetic Networks as Circuits With Resistance Distance

- Mathematics, Computer Science
- Frontiers in Genetics
- 2020

It is suggested that it can be useful to view unknown genetic distance along edges in phylogenetic networks as analogous to unknown resistance in electric circuits, which turns out to have nice mathematical properties which allow the precise reconstruction of networks. Expand

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