{"paper":{"title":"Vertical representation of $C^{\\infty}$-words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"cs.DM","authors_text":"Gabriele Fici, Jean-Marc F\\'edou","submitted_at":"2012-02-23T11:23:19Z","abstract_excerpt":"We present a new framework for dealing with $C^{\\infty}$-words, based on their left and right frontiers. This allows us to give a compact representation of them, and to describe the set of $C^{\\infty}$-words through an infinite directed acyclic graph $G$. This graph is defined by a map acting on the frontiers of $C^{\\infty}$-words. We show that this map can be defined recursively and with no explicit references to $C^{\\infty}$-words. We then show that some important conjectures on $C^{\\infty}$-words follow from analogous statements on the structure of the graph $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5154","kind":"arxiv","version":3},"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"}