2023/01/24 by Anwar Al Ghabra, K. Gopala Krishna, Ghabra, Anwar Al +5
Biochemistry, Genetics and Molecular Biology · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Markov Chains and Monte Carlo Methods #Protein Structure and Dynamics
paper · pdf · doi:10.48550/arxiv.2301.09765
openalex publication_date 2023/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give closed form expressions for the numbers of multi-rooted plane trees with specified degrees of root vertices. This results in an infinite number of integer sequences some of which are known to have an alternative interpretation. We also propose recursion relations for numbers of such trees as well as for the corresponding generating functions. Explicit expressions for the generating functions corresponding to plane trees having two and three roots are derived. As a by-product, we obtain a new binomial identity and a conjecture relating hypergeometric functions.