{"paper":{"title":"Inducibility in binary trees and crossings in random tanglegrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"\\'Eva Czabarka, L\\'aszl\\'o A. Sz\\'ekely, Stephan Wagner","submitted_at":"2016-01-26T20:14:37Z","abstract_excerpt":"In analogy to other concepts of a similar nature, we define the inducibility of a rooted binary tree. Given a fixed rooted binary tree $B$ with $k$ leaves, we let $\\gamma(B,T)$ be the proportion of all subsets of $k$ leaves in $T$ that induce a tree isomorphic to $B$. The inducibility of $B$ is $\\limsup_{|T| \\to \\infty} \\gamma(B,T)$. We determine the inducibility in some special cases, show that every binary tree has positive inducibility and prove that caterpillars are the only binary trees with inducibility $1$. We also formulate some open problems and conjectures on the inducibility. Finall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07149","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}