On the graph labellings arising from phylogenetics

DOI10.2478/s11533-013-0263-3zbMath1282.14087arXiv1105.5382OpenAlexW3098434817MaRDI QIDQ386402

Mateusz Michałek, Kaie Kubjas, Weronika Buczyńska, Jarosław Buczyński

Publication date: 9 December 2013

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.5382

zbMATH Keywords

Hilbert basis2-state Jukes-Cantor modelCavender-Farris-Neyman modelconformal block algebrasgraph labellingslattice conephylogenetic semigroupsemigroup generators

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Commutative semigroups (20M14) Free semigroups, generators and relations, word problems (20M05) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Related Items (7)

Finite phylogenetic complexity of \(\mathbb{Z}_p\) and invariants for \(\mathbb{Z}_3\) ⋮ Semigroup theory of symmetry ⋮ Compactifications of character varieties and skein relations on conformal blocks ⋮ The algebra of \(\mathrm{SL}_3(\mathbb{C})\) conformal blocks ⋮ Conformal blocks, Berenstein-Zelevinsky triangles, and group-based models ⋮ Toric fiber products versus Segre products ⋮ Low degree minimal generators of phylogenetic semigroups

Uses Software

• Magma

Cites Work

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• Phylogenetic toric varieties on graphs
• Coordinate rings for the moduli stack of \(\mathrm{SL}(\mathbb C)\) quasi-parabolic principal bundles on a curve and toric fiber products
• The algebra of \(\mathrm{SL}_3(\mathbb{C})\) conformal blocks
• On geometry of binary symmetric models of phylogenetic trees
• Phylogenetic invariants for group-based models
• Hilbert Polynomial of the Kimura 3-Parameter Model
• Statistics
• Toric Ideals of Phylogenetic Invariants
• Toric geometry of the 3-Kimura model for any tree

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