{"paper":{"title":"Encoding and avoiding 2-connected patterns in polygon dissections and outerplanar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vasiliki Velona","submitted_at":"2018-02-11T10:51:33Z","abstract_excerpt":"Let $\\Delta =\\{ \\delta_1,\\delta_2,...,\\delta_m \\} $ be a finite set of 2-connected patterns, i.e. graphs up to vertex relabelling. We study the generating function $D_{\\Delta }(z,u_1,u_2,...,u_m),$ which counts polygon dissections and marks subgraph copies of $\\delta_i$ with the variable $u_i$. We prove that this is always algebraic, through an explicit combinatorial decomposition depending on $\\Delta $. The decomposition also gives a defining system for $D_{\\Delta }(z,\\mathbf{0})$, which encodes polygon dissections that restrict these patterns as subgraphs. In this way, we are able to extract"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03719","kind":"arxiv","version":2},"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"}