id: 01177895
dt: j
an: 01177895
au: Prodinger, Helmut
ti: On a problem of Yekutieli and Mandelbrot about the bifurcation ratio of
    binary trees.
so: Theor. Comput. Sci. 181, No.1, 181-194 (1997).
py: 1997
pu: Elsevier Science Publishers, Amsterdam
la: EN
cc: 
ut: Horton-Strahler number; binary trees
ci: 
li: doi:10.1016/S0304-3975(96)00269-1
ab: Summary: Concerning the Horton-Strahler number (or register function) of
    binary trees, Yekutieli and Mandelbrot posed the problem of analyzing
    the bifurcation ratio of the root, which means how many maximal
    subtrees of register function one less than the whole tree are present
    in the tree. We show that if all binary trees of size n are considered
    to be equally likely, then the average value of this number of subtrees
    is asymptotic to $3.341266+ δ(\log_4 n)$, where an analytic expression
    for the numerical constant is available and $δ(x)$ is a (small)
    periodic function of period 1, which is also given explicitly.
    Additionally, we sketch the computation of the variance and also of
    higher bifurcation ratios.
rv: