{"paper":{"title":"Vertically constrained Motzkin-like paths inspired by bobbin lace","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Frank Ruskey, Stephen Melczer, Veronika Irvine","submitted_at":"2018-04-23T20:30:09Z","abstract_excerpt":"Inspired by a new mathematical model for bobbin lace, this paper considers finite lattice paths formed from the set of step vectors $\\mathfrak{A}=$$\\{\\rightarrow,$ $\\nearrow,$ $\\searrow,$ $\\uparrow,$ $\\downarrow\\}$ with the restriction that vertical steps $(\\uparrow, \\downarrow)$ cannot be consecutive. The set $\\mathfrak{A}$ is the union of the well known Motzkin step vectors $\\mathfrak{M}=$$\\{\\rightarrow,$ $\\nearrow,$ $\\searrow\\}$ with the vertical steps $\\{\\uparrow, \\downarrow\\}$. An explicit bijection $\\phi$ between the exhaustive set of vertically constrained paths formed from $\\mathfrak{A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08725","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"}