Enumeration of Weighted Plane Trees
Alexander K. Zvonkin
TL;DR
This paper presents a method for counting weighted bicolored plane trees based on their total weight and number of edges, providing a systematic enumeration approach.
Contribution
It introduces a novel enumeration technique specifically for weighted bicolored plane trees considering edge weights and counts.
Findings
Derived explicit formulas for enumeration
Established connections with combinatorial structures
Provided enumeration results for various weights
Abstract
In weighted trees, all edges are endowed with positive integral weight. We enumerate weighted bicolored plane trees according to their weight and number of edges.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Graph theory and applications · Advanced Graph Theory Research