{"paper":{"title":"Partial Geometric Designs from Group Actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jerod Michel, Qi Wang","submitted_at":"2018-07-26T08:06:01Z","abstract_excerpt":"In this paper, using group actions, we introduce a new method for constructing partial geometric designs (sometimes referred to as $1\\frac{1}{2}$-designs). Using this new method, we construct several infinite families of partial geometric designs by investigating the actions of various linear groups of degree two on certain subsets of $\\mathbb{F}_{q}^{2}$. Moreover, by computing the stabilizers of such subsets in various linear groups of degree two, we are also able to construct a new infinite family of balanced incomplete block designs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09998","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"}