{"paper":{"title":"The NF-operator and the NF-Numbers of Simplicial Complexes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math.AC"],"primary_cat":"math.CO","authors_text":"Bilal Ahmad Rather","submitted_at":"2026-05-29T03:12:33Z","abstract_excerpt":"Let $\\bigtriangleup$ be a simplicial complex and let $\\delta_{\\mathcal{NF}}$ denote the NF-operator. The NF-complex $\\delta_{\\mathcal{NF}}(\\bigtriangleup)$ is defined as the Stanley--Reisner complex of the facet ideal of $\\bigtriangleup$. Iterating $\\delta_{\\mathcal{NF}}$ gives a periodic orbit (up to isomorphism), and the smallest positive integer $t$ for which $\\delta_{\\mathcal{NF}}^{\\,t}(\\bigtriangleup)\\cong \\bigtriangleup$ is called the \\emph{NF-number} of $\\bigtriangleup$ (Habi and Mahmood, Algebra Colloquium, 2022). In this work, we provide various results and determine explicit formulas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30781","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.30781/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"}