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Phylogenetic Trees03:21

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Updated: May 16, 2026

Visualizing Lignification Dynamics in Plants with Click Chemistry: Dual Labeling is BLISS!
10:40

Visualizing Lignification Dynamics in Plants with Click Chemistry: Dual Labeling is BLISS!

Published on: January 26, 2018

Generating Functions for Multi-labeled Trees.

E Czabarka1, P L Erdős, V Johnson

  • 1Department of Mathematics, University of South Carolina, Columbia, SC 29208, Phone:+1-803-777-7524, FAX: +1-803-777-3783.

Discrete Applied Mathematics (Amsterdam, Netherlands : 1988)
|November 24, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces multi-labeled trees, a novel type of phylogenetic tree, and provides formulas for counting them. These findings generalize existing theorems in evolutionary biology and network construction.

Related Experiment Videos

Last Updated: May 16, 2026

Visualizing Lignification Dynamics in Plants with Click Chemistry: Dual Labeling is BLISS!
10:40

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Published on: January 26, 2018

Area of Science:

  • Evolutionary Biology
  • Computational Biology
  • Graph Theory

Background:

  • Phylogenetic trees are fundamental in understanding evolutionary relationships.
  • Multi-labeled trees extend phylogenetic trees, allowing multiple leaves to share the same label.
  • These structures are crucial for studying gene-species co-evolution and building phylogenetic networks.

Purpose of the Study:

  • To derive formulae for generating functions of leaf-multi-labeled trees.
  • To establish recursions for counting these generalized tree structures.
  • To extend foundational theorems in phylogenetic tree counting and analysis.

Main Methods:

  • Derivation of generating function formulae for leaf-multi-labeled trees.
  • Development of recursive methods for enumerating these trees.
  • Generalization of existing theorems on tree-shapes and rooted/unrooted tree counts.

Main Results:

  • New formulae for generating functions of leaf-multi-labeled trees.
  • Novel recursions for counting leaf-multi-labeled trees.
  • Generalizations of Harding's theorems on tree-shapes and Otter's theorems relating rooted and unrooted trees.

Conclusions:

  • The study provides a combinatorial framework for analyzing multi-labeled trees.
  • The derived formulae and recursions offer powerful tools for phylogenetic analysis.
  • This work advances the understanding of tree structures in evolutionary and computational biology.