Work

The shape of random tanglegrams

Year: 2015

Type: preprint

Abstract: A tanglegram consists of two binary rooted trees with the same number of leaves and a perfect matching between the leaves of the trees. We show that the two halves of a random tanglegram essentially look like two independently chosen random plane binary trees. This fact is used to derive a number of results on the shape of random tanglegrams, including theorems on the number of cherries and generally occurrences of subtrees, the root branches, the number of automorphisms, and the height. For each of these, we obtain limiting probabilities or distributions. Finally, we investigate the number of matched cherries, for which the limiting distribution is identified as well.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1512.01168

Authors: Konvalinka, Matjaž, Wagner, Stephan

Institutions: University of Ljubljana, Institute of Mathematics, Physics, and Mechanics, Stellenbosch University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Research Foundation, Javna Agencija za Raziskovalno Dejavnost RS

Awards: G3815100896, Pieri rules for Hall-Littlewood polynomials and Macdonald polynomials

OpenAlex ID: W2952659921

Cites: 8

Cited by: 3

Related to: 20