{"paper":{"title":"Circular planar nearrings: geometrical and combinatorial aspects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RA","authors_text":"Achille Frigeri, Anna Benini, Fiorenza Morini","submitted_at":"2010-12-06T00:44:28Z","abstract_excerpt":"Let $(N,\\Phi)$ be a circular Ferrero pair. We define the disk with center $b$ and radius $a$, $\\mathcal{D}(a;b)$, as \\[\\mathcal{D}(a;b)=\\{x\\in \\Phi(r)+c\\mid r\\neq 0,\\ b\\in \\Phi(r)+c,\\ |(\\Phi(r)+c)\\cap (\\Phi(a)+b)|=1\\}.\\] We prove that in the field-generated case there are many analogies with the Euclidean geometry. Moreover, if $\\mathcal{B}^{\\mathcal{D}}$ is the set of all disks, then, in some interesting cases, we show that the incidence structure $(N,\\mathcal{B}^{\\mathcal{D}},\\in)$ is actually a balanced incomplete block design."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1059","kind":"arxiv","version":5},"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"}