{"paper":{"title":"On the number of L-shapes in embedding dimension four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. Llena, F. Aguil\\'o-Gost, P. A. Garc\\'ia-S\\'anchez","submitted_at":"2015-05-06T19:11:05Z","abstract_excerpt":"\\textit{Minimum distance diagrams}, also known as \\textit{\\textsf{L}--shapes}, have been used to study some properties related to \\textit{weighted Cayley digraphs} of \\textit{degree} two and \\textit{embedding dimension three numerical semigroups}. In this particular case, it has been shown that these discrete structures have at most two related \\textsf{L}--shapes. These diagrams are proved to be a good tool for studing \\textit{factorizations} and the \\textit{catenary degree} for semigroups and \\textit{diameter} and \\textit{distance} between vertices for digraphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01464","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"}