OFFSET

4,1

COMMENTS

The balanced minimum evolution (BME) polytope of order n is a polytope in binom(n, 2)-dimensional space whose vertices are indexed by bifurcating phylogenetic trees on n species. The coordinates of the ambient space are indexed by pairs (i, j) of distinct species, and at a vertex corresponding to tree T, the value at coordinate (i, j) is equal to 2^-k(i, j) where k(i, j) is the number of internal nodes on the path from i to j in T.

LINKS

Stefan Forcey, Encyclopedia of Combinatorial Polytope Sequences: Balanced Minimum Evolution Polytope.

Stefan Forcey, Logan Keefe, and William Sands, Split-Facets for Balanced Minimum Evolution Polytopes and the Permutoassociahedron, Bull. Math. Biol., 79 (2017), 975-994.

CROSSREFS

KEYWORD

nonn,more,bref

AUTHOR

Harry Richman, Jul 24 2023

STATUS

approved