(none)

zharkikh at GSBS18.GS.UTH.TMC.EDU zharkikh at GSBS18.GS.UTH.TMC.EDU
Wed Jun 22 10:24:02 EST 1994



Frank,
this problem was solved many times (I do not remember who and when).
You can list all possible trees when you construct them by adding
one species at a time. For 3 taxa, there is a single topology.
Add the fourth taxon to one of the three branches (three ways).
You will get a tree of four taxa which has 5 branches.
Add the fifth taxon to one of the five branches (five ways).
And so on...
Each time you will add a new taxon to a tree of K taxa which
has 2K-3 branches. The total number of ways is the product of
(2K-3) for K=3,...,N-1.

This gives

N=4    (2*3-3)=3
N=5    3*(2*4-3)=15
N=6    15*(2*5-3)=105
...

Good luck!

Andrey





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