{"paper":{"title":"On the metric dimension of affine planes, biaffine planes and generalized quadrangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniele Bartoli, Gy\\\"orgy Kiss, Marcella Tak\\'ats, Tam\\'as H\\'eger","submitted_at":"2017-06-20T15:16:13Z","abstract_excerpt":"In this paper the metric dimension of (the incidence graphs of) particular partial linear spaces is considered. We prove that the metric dimension of an affine plane of order $q\\geq13$ is $3q-4$ and describe all resolving sets of that size if $q\\geq 23$. The metric dimension of a biaffine plane (also called a flag-type elliptic semiplane) of order $q\\geq 4$ is shown to fall between $2q-2$ and $3q-6$, while for Desarguesian biaffine planes the lower bound is improved to $8q/3-7$ under $q\\geq 7$, and to $3q-9\\sqrt{q}$ under certain stronger restrictions on $q$. We determine the metric dimension "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06583","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":""},"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"}