Phylogenetic toric varieties on graphs. (English) Zbl 1376.14050
Summary: We define phylogenetic projective toric model of a trivalent graph as a generalization of a binary symmetric model of a trivalent phylogenetic tree. Generators of the projective coordinate ring of the models of graphs with one cycle are explicitly described. The phylogenetic models of graphs with the same topological invariants are deformation-equivalent and share the same Hilbert function. We also provide an algorithm to compute the Hilbert function.
MSC:
| 14L24 | Geometric invariant theory |
| 14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
| 13P25 | Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) |
| 13D40 | Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series |
| 92D15 | Problems related to evolution |
Software:
MagmaReferences:
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