Split-Facets for Balanced Minimal Evolution Polytopes and the Permutoassociahedron

Autor: Logan Keefe, Stefan Forcey, William Sands
Rok vydání: 2017
Předmět:
0301 basic medicine
General Mathematics
Immunology
0211 other engineering and technologies
Polytope
02 engineering and technology
General Biochemistry
Genetics and Molecular Biology
Combinatorics
03 medical and health sciences
Rectification
Lattice (order)
FOS: Mathematics
Mathematics - Combinatorics
Mathematics::Metric Geometry
Quantitative Biology::Populations and Evolution
Phylogeny
Quotient
General Environmental Science
Mathematics
Pharmacology
Discrete mathematics
Mathematics::Combinatorics
021103 operations research
Models
Genetic
Birkhoff polytope
General Neuroscience
Uniform k 21 polytope
Mathematical Concepts
Biological Evolution
Quantitative Biology::Genomics
030104 developmental biology
90C05
52B11
92D15
Computational Theory and Mathematics
Combinatorics (math.CO)
General Agricultural and Biological Sciences
Partially ordered set
Algorithms
Maximal element
Zdroj: Bulletin of Mathematical Biology. 79:975-994
ISSN: 1522-9602
0092-8240
DOI: 10.1007/s11538-017-0264-7
Popis: Understanding the face structure of the balanced minimal evolution (BME) polytope, especially its top-dimensional facets, is crucially important to phylogenetic applications. We show that BME polytope has a sub-lattice of its poset of faces which is isomorphic to a quotient of the well-studied permutoassociahedron. This sub-lattice corresponds to compatible sets of splits displayed by phylogenetic trees, and extends the lattice of faces of the BME polytope found by Hodge, Haws, and Yoshida. Each of the maximal elements in our new poset of faces corresponds to a single split of the leaves. Nearly all of these turn out to actually be facets of the BME polytope, a collection of facets which grows exponentially.
Databáze: OpenAIRE
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