{"paper":{"title":"Distribution of determinant of sum of matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Anh Vinh Le, Daewoong Cheong, Doowon Koh, Thang Pham","submitted_at":"2019-04-16T17:51:28Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be an arbitrary finite field of order $q$. In this article, we study $\\det S$ for certain types of subsets $S$ in the ring $M_2(\\mathbb F_q)$ of $2\\times 2$ matrices with entries in $\\mathbb F_q$. For $i\\in \\mathbb{F}_q$, let $D_i$ be the subset of $M_2(\\mathbb F_q)$ defined by\n  $ D_i := \\{x\\in M_2(\\mathbb F_q): \\det(x)=i\\}.$ Then our results can be stated as follows. First of all, we show that when $E$ and $F$ are subsets of $D_i$ and $D_j$ for some $i, j\\in \\mathbb{F}_q^*$, respectively, we have $$\\det(E+F)=\\mathbb F_q,$$ whenever $|E||F|\\ge {15}^2q^4$, and then provide a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07847","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"}