Low degree minimal generators of phylogenetic semigroups
Combinatorics
2013-04-03 v1 Algebraic Geometry
Abstract
The phylogenetic semigroup on a graph generalizes the Jukes-Cantor binary model on a tree. Minimal generating sets of phylogenetic semigroups have been described for trivalent trees by Buczy\'nska and Wi\'sniewski, and for trivalent graphs with first Betti number 1 by Buczy\'nska. We characterize degree two minimal generators of the phylogenetic semigroup on any trivalent graph. Moreover, for any graph with first Betti number 1 and for any trivalent graph with first Betti number 2 we describe the minimal generating set of its phylogenetic semigroup.
Keywords
Cite
@article{arxiv.1304.0744,
title = {Low degree minimal generators of phylogenetic semigroups},
author = {Kaie Kubjas},
journal= {arXiv preprint arXiv:1304.0744},
year = {2013}
}