{"paper":{"title":"Eventually, geometric $(n_{k})$ configurations exist for all $n$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"(2) Bolyai Institute, (3) University of Primorska, G\\'abor G\\'evay (2), Institute of Mathematics, Leah Wrenn Berman (1), Mechanics, Physics, Toma\\v{z} Pisanski (3) ((1) University of Alaska Fairbanks, University of Ljubljana), University of Szeged","submitted_at":"2021-03-31T18:15:20Z","abstract_excerpt":"In a series of papers and in his 2009 book on configurations Branko Gr\\\"unbaum described a sequence of operations to produce new $(n_{4})$ configurations from various input configurations. These operations were later called the \"Gr\\\"unbaum Incidence Calculus\". We generalize two of these operations to produce operations on arbitrary $(n_{k})$ configurations. Using them, we show that for any $k$ there exists an integer $N_k$ such that for any $n \\geq N_k$ there exists a geometric $(n_k)$ configuration. We use empirical results for $k = 2, 3, 4$, and some more detailed analysis to improve the upp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.00045","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/2104.00045/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"}