{"paper":{"title":"Counting mountain-valley assignments for flat folds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Thomas C. Hull","submitted_at":"2014-10-19T01:26:30Z","abstract_excerpt":"We develop a combinatorial model of paperfolding for the purposes of enumeration. A planar embedding of a graph is called a {\\em crease pattern} if it represents the crease lines needed to fold a piece of paper into something. A {\\em flat fold} is a crease pattern which lies flat when folded, i.e. can be pressed in a book without crumpling. Given a crease pattern $C=(V,E)$, a {\\em mountain-valley (MV) assignment} is a function $f:E\\rightarrow \\{$M,V$\\}$ which indicates which crease lines are convex and which are concave, respectively. A MV assignment is {\\em valid} if it doesn't force the pape"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5022","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"}