Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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PICK TWO POINTS IN A TREE

  • Kim, Hana (Applied Algebra and Optimization Research Center Sungkyunkwan University) ;
  • Shapiro, Louis W. (Department of Mathematics Howard University)
  • Received : 2018.07.25
  • Accepted : 2018.10.11
  • Published : 2019.09.01
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Abstract

In ordered trees, two randomly chosen vertices are said to be dependent if one lies under the other. If not, we say that they are independent. We consider several classes of ordered trees with uniform updegree requirements and find the generating functions for the trees with two marked dependent/independent vertices. As a result, we compute the probability for two vertices being dependent/independent. We also count such trees by the distance between two independent vertices.

Keywords

DBSHBB_2019_v56n5_1247_f0001.png 이미지

FIGURE 1. Distribution of pairs of leaves in complete binary trees with 10 edges by distance.

DBSHBB_2019_v56n5_1247_f0002.png 이미지

FIGURE 2. Distribution of complete binary trees with two marked leaves at a given distance by the number of edges. Di erent colors are used to distinguish the distances between two leaves.

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