{"paper":{"title":"Characterizing and Transforming DAGs within the I-LCA Framework","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anna Lindeberg, Marc Hellmuth","submitted_at":"2024-11-21T12:09:21Z","abstract_excerpt":"We explore the connections between clusters and least common ancestors (LCAs) in directed acyclic graphs (DAGs), focusing on the interplay between so-called $I$-lca-relevant DAGs and DAGs with the $I$-lca-property. Here, $I$ denotes a set of integers. In $I$-lca-relevant DAGs, each vertex is the unique LCA for some subset $A$ of leaves of size $|A|\\in I$, whereas in a DAG with the $I$-lca-property there exists a unique LCA for every subset $A$ of leaves satisfying $|A|\\in I$. We elaborate on the difference between these two properties and establish their close relationship to pre-$I$-ary and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14057","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.14057/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}