{"paper":{"title":"$k$-Foldability of Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Beth Bjorkman, Danny Rorabaugh, Garner Cochran, Heather Smith, Jennifer Wise, Lauren Keough, Mitch Phillipson, Rachel Kirsch, Wei Gao","submitted_at":"2017-10-29T13:44:59Z","abstract_excerpt":"We extend results regarding a combinatorial model introduced by Black, Drellich, and Tymoczko (2017+) which generalizes the folding of the RNA molecule in biology. Consider a word on alphabet $\\{A_1, \\overline{A}_1, \\ldots, A_m, \\overline{A}_m\\}$ in which $\\overline{A}_i$ is called the complement of $A_i$. A word $w$ is foldable if can be wrapped around a rooted plane tree $T$, starting at the root and working counterclockwise such that one letter labels each half edge and the two letters labeling the same edge are complements. The tree $T$ is called $w$-valid.\n  We define a bijection between "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10616","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"}