Figure 2: A reticulate tree
1 2 3 ...............................................N
Figure 3: N-ary branching
1.5 Reticulate & N-ary Trees
A reticulate tree is a tree in which there are one or more sets of reconvergent
branches, illustrated by Figure 2, a non-reticulate tree is a tree in which
the branches do not reconverge. N-ary branching is illustrated by Figure 3.
Binary branching is N-ary branching with N = 2. N-ary branching can
be replaced by binary branching if additional layers are used. A switched
tree is a tree in which all the branches are binary. Syntactic phrase trees
are non-reticulate and switched. In most linguistic theories all syntac-
tic phrase trees have X structure, Jackendoff (1977) [16]. X structure implies
binary branching, see subsectionxbt and figure 8 Here attention is restricted to
theory which has JX structure.
1.6 Sectional Contents
In section 2 it is shown how to represent trees by matrices and triangles. All
JX triangles are isosceles but not equilateral. In section 3 the matrix U for
the minimum ultrametric distance for lexical categories is given. For simplic-