{"paper":{"title":"Laplacian Simplices II: A Coding Theoretic Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marie Meyer, Tefjol Pllaha","submitted_at":"2018-09-09T12:19:38Z","abstract_excerpt":"This paper further investigates \\emph{Laplacian simplices}. A construction by Braun and the first author associates to a simple connected graph $G$ a simplex $\\cP_G$ whose vertices are the rows of the Laplacian matrix of $G$. In this paper we associate to a reflexive $\\cP_G$ a duality-preserving linear code $\\cC(\\cP_G)$. This new perspective allows us to build upon previous results relating graphical properties of $G$ to properties of the polytope $\\cP_G$. In particular, we make progress towards a graphical characterization of reflexive $\\cP_G$ using techniques from Ehrhart theory. We provide "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02960","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"}