{"paper":{"title":"The Cellular Homology of Digraphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Shing-Tung Yau, Xinxing Tang","submitted_at":"2024-02-08T13:59:27Z","abstract_excerpt":"In \\cite{TY}, we investigate the pair $(P, \\Supp(P))$ of minimal path $P$ and its supporting sub-digraph $\\Supp(P)$ in the path complex of a digraph $G$ under the strongly regular condition. In this paper, first, we consider the special minimal path $P$ specified by the admissible condition (Definition \\ref{admpair}), which means that $(P,\\Supp(P))$ admits a singular cubical realization. Based on such a subset, we systematically introduce the definitions of cellular chain complex associated to $G$ and prove the well-definedness. Then we study several properties of such cellular homologies. Fin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.05682","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/2402.05682/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"}