{"paper":{"title":"On some generalization of the M\\\"obius configuration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Krzysztof Petelczyc","submitted_at":"2013-10-03T15:08:27Z","abstract_excerpt":"The M\\\"obius $(8_4)$ configuration is generalized in a purely combinatorial approach. We consider $(2n_n)$ configurations ${\\goth M}_{(n,\\varphi)}$ depending on a permutation $\\varphi$ in the symmetric group $S_n$. Classes of non-isomorphic configurations of this type are determined. The parametric characterization of ${\\goth M}_{(n,\\varphi)}$ is given. The uniqueness of the decomposition of ${\\goth M}_{(n,\\varphi)}$ into two mutually inscribed $n$-simplices is discussed. The automorphisms of ${\\goth M}_{(n,\\varphi)}$ are characterized for $n\\geq 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1004","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"}