{"paper":{"title":"Universal and Overlap Cycles for Posets, Words, and Juggling Patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adam King, Amanda Laubmeier, Anant Godbole, Kai Orans","submitted_at":"2014-05-23T00:30:53Z","abstract_excerpt":"We discuss results dealing with universal cycles (u-cycles) and $s$-overlap cycles, and contribute to the body of those results by proving existence of universal cycles of naturally labeled posets (NL posets), $s$-overlap cycles of words of weight $k$, and juggling patterns. The result on posets is, to the best of our knowledge, the first demonstration of the existence of a u-cycle whose length is unknown."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5938","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"}