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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.
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참고문헌 (10)
참고문헌 신청
Gi-Sang Cheon / 2016 / Profiles of ordered trees with mutation and associated Riordan matrices / Linear Algebra and its Applications 511:296~317
Gi-Sang Cheon / 2008 / Protected points in ordered trees / Applied Mathematics Letters 21(5):516~520
M. Drmota / 2009 / Random Trees / Springer Verlag
P. Flajolet / 2009 / Analytic Combinatorics / Cambridge University Press
R. L. Graham / 1994 / Concrete Mathematics, second edition / Addison-Wesley Publishing Company
Gi-Sang Cheon / 2008 / Protected points in ordered trees / Applied Mathematics Letters 21(5):516~520
M. Drmota / 2009 / Random Trees / Springer Verlag
P. Flajolet / 2009 / Analytic Combinatorics / Cambridge University Press
R. L. Graham / 1994 / Concrete Mathematics, second edition / Addison-Wesley Publishing Company
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