2024/10/19 by Chloe E. Shiff, Noah A. Rosenberg, Shiff, Chloe E. +1
Computer Science · Mathematics · #05A15 #05A16 #05C05 #92D15 #Advanced Combinatorial Mathematics #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Biological sciences #FOS: Mathematics #Populations and Evolution (q-bio.PE) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2410.14915
openalex publication_date 2024/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Rooted binary perfect phylogenies provide a generalization of rooted binary unlabeled trees in which each leaf is assigned a positive integer value that corresponds in a biological setting to the count of the number of indistinguishable lineages associated with the leaf. For the rooted binary unlabeled trees, these integers equal 1. We address a variety of enumerative problems concerning rooted binary perfect phylogenies with sample size s: the rooted binary unlabeled trees in which a sample of size s lineages is distributed across the leaves of an unlabeled tree with n leaves, 1 ≤ n ≤ s. The enumerations further characterize the rooted binary perfect phylogenies, which include the rooted binary unlabeled trees, and which can provide a set of structures useful for various biological contexts.