
Nonsymmetric Operads 77
Int(τ
1
◦
`
τ
2
) = Int(τ
1
) tInt(τ
2
),
Leaves(τ
1
◦
`
τ
2
) = Leaves(τ
1
) tLeaves(τ
2
) \{}.
The parent function and the planar structure on the thus defined set of
vertices are induced by the respective parent functions and planar struc-
tures of τ
1
and τ
2
with two small exceptions. For the only vertex v in
Parent
−1
τ
2
(Root(τ
2
)), we define Parent
τ
1
◦
`
τ
2
(v) = Parent
τ
1
(). This means that
Parent
−1
τ
1
◦
`
τ
2
(Parent
τ
1
()) = {v}tParent
−1
τ
1
(Parent
τ
1
()) \{}; the total order
needed by the planar structure puts v in the place of .
Example 3.3.3.3. Let τ
1
= and τ
2
= . Various partial compo-
sitions of these trees are summarized in the following table:
τ
1
◦
1
τ
2
τ