![]() ![]() Lovacz (ed.), Handbook of Combinatorics, II, Elsevier (1995) pp. All the nodes in a complete binary tree are as far left as possible. Comtet, "Advanced combinatorics", Reidel (1974) A Complete Binary tree is a binary tree in which every level, except possibly the last, is completely filled. Catalan, "Note sur une équation aux différences finies" J. ![]() The correspondence between complete binary trees and (complete) bracketings gives a bijection between complete binary trees with leaves labelled with elements from a set $X$ and the free magma on $X$.Į. The problem of all such bracketings of a product (of numbers) was considered by E. The number of binary trees with $n$ nodes, $p$ left children, $q$ right children ($p+q=n-1$) is 2010 Mathematics Subject Classification: Primary: 05C05 Ī (planar) rooted tree for which every node has a left child, a right child, neither, or both. ![]()
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