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Number of facets of the balanced minimum evolution polytope on n species.

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`%I #21 Sep 06 2023 06:58:21
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`%S 3,52,90262
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`%N Number of facets of the balanced minimum evolution polytope on n species.
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`%C 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.
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`%H Stefan Forcey, <a href="https://sforcey.github.io/sf34/hedra.htm#BME">Encyclopedia of Combinatorial Polytope Sequences: Balanced Minimum Evolution Polytope</a>.
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`%H Stefan Forcey, Logan Keefe, and William Sands, <a href="https://doi.org/10.1007/s11538-017-0264-7">Split-Facets for Balanced Minimum Evolution Polytopes and the Permutoassociahedron</a>, Bull. Math. Biol., 79 (2017), 975-994.
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`%Y Cf. A364505.
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`%K nonn,more,bref
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`%O 4,1
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`%A _Harry Richman_, Jul 24 2023
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