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In graph theory, a recursive tree (i.e., unordered tree) is a non-planar labeled rooted tree. A size-''n'' recursive tree is labeled by distinct integers 1, 2, ..., ''n'', where the labels are strictly increasing starting at the root labeled 1. Recursive trees are non-planar, which means that the children of a particular node are not ordered. E.g. the following two size-three recursive trees are the same.
Recursive trees also appear in literature under the name Increasing Cayley trees. ==Properties == The number of size-''n'' recursive trees is given by : Hence the exponential generating function ''T''(''z'') of the sequence ''T''''n'' is given by : Combinatorically a recursive tree can be interpreted as a root followed by an unordered sequence of recursive trees. Let ''F'' denote the family of recursive trees. : where denotes the node labeled by 1, × the Cartesian product and the partition product for labeled objects. By translation of the formal description one obtains the differential equation for ''T''(''z'') : with ''T''(0) = 0. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Recursive tree」の詳細全文を読む スポンサード リンク
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