Tree evolution processes for bucket increasing trees

2022/06/10 by Markus Kuba, Kuba, Markus, Alois Panholzer +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #05A15 #05A19 #05C05 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Probability (math.PR) #Protein Structure and Dynamics

paper · pdf · doi:10.48550/arxiv.2206.05101

openalex publication_date 2022/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a fundamental result for bucket increasing trees, which gives a complete characterization of all families of bucket increasing trees that can be generated by a tree evolution process. We also provide several equivalent properties, complementing and extending earlier results for ordinary increasing trees to bucket trees. Additionally, we state second order results for the number of descendants of label j, again extending earlier results in the literature.

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