NPartitionPairs() calculates the number of terminal arrangements matching a specified configuration of two splits.

NPartitionPairs(configuration)

Arguments

configuration

Integer vector of length four specifying the number of terminals that occur in both (1) splits A1 and A2; (2) splits A1 and B2; (3) splits B1 and A2; (4) splits B1 and B2.

Value

The number of ways to distribute sum(configuration) taxa according to the specified pattern.

Details

Consider splits that divide eight terminals, labelled A to H.

Bipartition 1:ABCD:EFGHA1 = ABCDB1 = EFGH
Bipartition 2:ABE:CDFGHA2 = ABEB2 = CDFGH

This can be represented by an association matrix:

A2B2
A1ABC
B1EFGH

The cells in this matrix contain 2, 1, 1 and 3 terminals respectively; this four-element vector (c(2, 1, 1, 3)) is the configuration implied by this pair of bipartition splits.

Author

Martin R. Smith (martin.smith@durham.ac.uk)

Examples

NPartitionPairs(c(2, 1, 1, 3))
#> [1] 12