A bijection between phylogenetic trees and plane oriented recursive trees

DOI10.13137/2464-8728/22432zbMATH Open1444.05042arXiv1709.05966OpenAlexW2754310603MaRDI QIDQ3297879

Helmut Prodinger

Publication date: 21 July 2020

Abstract: Phylogenetic trees are binary nonplanar trees with labelled leaves, and plane oriented recursive trees are planar trees with an increasing labelling. Both families are enumerated by double factorials. A bijection is constructed, using the respective representations a 2-partitions and trapezoidal words.

Full work available at URL: https://arxiv.org/abs/1709.05966

zbMATH Keywords

bijectionphylogenetic treetrapezoidal wordplane oriented recursive tree

Mathematics Subject Classification ID

Trees (05C05) Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Enumeration in graph theory (05C30) Graph labelling (graceful graphs, bandwidth, etc.) (05C78)

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