{"paper":{"title":"q-Analogs of Steiner Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Vardy, Tuvi Etzion","submitted_at":"2012-11-11T10:03:05Z","abstract_excerpt":"A Steiner structure $\\dS = \\dS_q[t,k,n]$ is a set of $k$-dimensional subspaces of $\\F_q^n$ such that each $t$-dimensional subspace of $\\F_q^n$ is contained in exactly one subspace of $\\dS$. Steiner structures are the $q$-analogs of Steiner systems; they are presently known to exist only for $t = 1$, $t=k$, and\\linebreak for $k = n$. The existence of nontrivial $q$-analogs of Steiner systems has occupied mathematicians for over three decades. In fact, it was conjectured that they do not exist.\n  In this paper, we show that nontrivial Steiner structures do exist. First, we describe a general met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2393","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"}