\section{Variation: Ternary trees}
Let us now try a variation on lexicon structure, using the notion of a
ternary tree.
This notion is fairly natural if one wants to restore for ordered trees
the locality of zipper navigation in binary trees. Remark that when we
go up to the current father, we have to close the list of elder siblings
in order to restore the full list of children of the upper node.
With ternary trees each tree node has two lists of children, elders and
youngers. When we go up in the zipper structure, it is now a constant
cost operation. Remark that this partition into elders and youngers is
not intrinsic and carries no information, except the memory of the previous
navigation. This is again an idea of optimizing computation by
creating redundancy in the data structure representations. We may for instance
exploit this redundancy in balancing our trees for faster access.
Ternary trees are inspired from Bentley and Sedgewick\cite{bentley}.