
Entropy rates for Horton selfsimilar trees
In this paper we examine planted binary plane trees. First, we provide a...
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Compaction for two models of logarithmicdepth trees: Analysis and Experiments
In this paper we are interested in the quantitative analysis of the comp...
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On the enumeration of plane bipolar posets and transversal structures
We show that plane bipolar posets (i.e., plane bipolar orientations with...
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On the Collection of Fringe Subtrees in Random Binary Trees
A fringe subtree of a rooted tree is a subtree consisting of one of the ...
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A OnetoOne Correspondence between Natural Numbers and Binary Trees
A characterization is provided for each natural number except one (1) by...
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Approximation by Lexicographically Maximal Solutions in Matching and Matroid Intersection Problems
We study how good a lexicographically maximal solution is in the weighte...
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A family of nonperiodic tilings of the plane by right golden triangles
We consider tilings of the plane by two prototiles which are right trian...
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Counting embeddings of rooted trees into families of rooted trees
The number of embeddings of a partially ordered set S in a partially ordered set T is the number of subposets of T isomorphic to S. If both, S and T, have only one unique maximal element, we define good embeddings as those in which the maximal elements of S and T overlap. We investigate the number of good and all embeddings of a rooted poset S in the family of all binary trees on n elements considering two cases: plane (when the order of descendants matters) and nonplane. Furthermore, we study the number of embeddings of a rooted poset S in the family of all planted plane trees of size n. We derive the asymptotic behaviour of good and all embeddings in all cases and we prove that the ratio of good embeddings to all is of the order Θ(1/√(n)) in all cases, where we provide the exact constants. Furthermore, we show that this ratio is nondecreasing with S in the plane binary case and asymptotically nondecreasing with S in the nonplane binary case and in the planted plane case. Finally, we comment on the case when S is disconnected.
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