{"paper":{"title":"Inducibility of d-ary trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Audace A.V. Dossou-Olory, \\'Eva Czabarka, L\\'aszl\\'o A. Sz\\'ekely, Stephan Wagner","submitted_at":"2018-02-11T21:00:40Z","abstract_excerpt":"Imitating a recently introduced invariant of trees, we initiate the study of the inducibility of $d$-ary trees (rooted trees whose vertex outdegrees are bounded from above by $d\\geq 2$) with a given number of leaves. We determine the exact inducibility for stars and binary caterpillars. For $T$ in the family of strictly $d$-ary trees (every vertex has $0$ or $d$ children), we prove that the difference between the maximum density of a $d$-ary tree $D$ in $T$ and the inducibility of $D$ is of order $\\mathcal{O}(|T|^{-1/2})$ compared to the general case where it is shown that the difference is $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03817","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"}