{"paper":{"title":"Constructing de Bruijn sequences by concatenating smaller universal cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Gabric, Joe Sawada","submitted_at":"2018-03-23T23:17:50Z","abstract_excerpt":"We present sufficient conditions for when an ordering of universal cycles $\\alpha_1, \\alpha_2, \\ldots, \\alpha_m$ for disjoint sets $\\mathbf{S}_1, \\mathbf{S}_2, \\ldots , \\mathbf{S}_m$ can be concatenated together to obtain a universal cycle for $\\mathbf{S} = \\mathbf{S}_1 \\cup \\mathbf{S}_2 \\cup \\cdots \\cup \\mathbf{S}_m$. When $\\mathbf{S}$ is the set of all $k$-ary strings of length $n$, the result of such a successful construction is a de Bruijn sequence. Our conditions are applied to generalize two previously known de Bruijn sequence constructions and then they are applied to develop three new "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09009","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"}