A364441 -id:A364441 - cp's OEIS frontend

A364505 T(n, k) = number of k-dimensional faces in the BME polytope on n species, 0 <= k <= binomial(n, 2) - n.

3, 3, 1, 15, 105, 250, 210, 52, 1, 105, 5460, 105945, 635265, 1715455, 2373345, 1742445, 640140, 90262, 1

Offset: 4

Harry Richman, Jul 26 2023

The balanced minimum evolution (BME) polytope of order n is the convex hull of the BME vectors of all phylogenetic trees on n species. The BME polytope of order n has dimension binomial(n, 2) - n.

			Table begins:
    3,    3,      1;
   15,  105,    250,    210,      52,       1;
  105, 5460, 105945, 635265, 1715455, 2373345, 1742445, 640140, 90262, 1;

Maria Angelica Cueto and Frederick A. Matsen, Polyhedral geometry of phylogenetic rogue taxa, Bull. Math. Biol., 73 (2011), 1202-1226.
K. Eickmeyer, P. Huggins, L. Pachter, and R. Yoshida, On the optimality of the neighbor-joining algorithm, Algorithms Mol Biol. 3 (2008), Article number 5.
Stefan Forcey, Balanced Minimum Evolution Polytope, Encyclopedia of Combinatorial Polytope Sequences (Hedra Zoo).

First column T(n, 0) is A001147.

Next-to-last entry T(n, binomial(n, 2) - n - 1) in each row is A364441.

cp's OEIS Frontend

A364505 T(n, k) = number of k-dimensional faces in the BME polytope on n species, 0 <= k <= binomial(n, 2) - n.

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