On The Joint Asymptotic Normality of Node Counts in Ordered Trees
By Yonah Biers-Ariel
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First Written: April 23, 2018; This version: May 14, 2018.
Abstract:
We provide a Maple package which examines the number of vertices with a particular number of children in a random ordered tree where all vertices must have a number of children in some finite set. By calculating the mixed moments of two such numbers, the package produces strong evidence that the numbers are pairwise asymptotically normal.
Maple packages
Sample Input and Output for ChildCountStatistics.txt
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If you want to see an article about the joint normality of the number of vertices with various numbers of children in trees on 60 vertices where all vertices have 0,1, or 2 children,
the input file generates the
output file.
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If you want to see an article about the joint normality of the number of vertices with various numbers of children in trees on 50 vertices where all vertices have 0,1, or 3 children,
the input file generates the
output file.
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If you want to see an article about the joint normality of the number of vertices with various numbers of children in trees on 50 vertices where all vertices have 0,2,3, or 4 children,
the input file generates the
output file.
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If you want to see an article about the joint normality of the number of vertices with various numbers of children in trees on 50 vertices where all vertices have 0,1,3, or 5 children,
the input file generates the
output file.
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If you want to see an article about the joint normality of the number of vertices with various numbers of children in trees on 30 vertices where all vertices have no more than 5 children,
the input file generates the
output file.