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K-Noncrossing Trees and K-Proper Trees

Tree structures play an important role in computer science. For instance, the binary tree is a fundamental data structure for rapidly storing sorted data and rapidly retrieving stored data. In this paper, we establish the structures of k-noncrossing trees and k-proper trees. Moreover, the relations between these structures and k-ary trees are also constructed. It exposes that such structures may be employed as efficient data structures for computer and information science.