{"paper":{"title":"Vertex-weighted graphs and freeness of $ \\psi $-graphical arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daisuke Suyama, Shuhei Tsujie","submitted_at":"2015-11-16T07:46:43Z","abstract_excerpt":"Let $ G $ be a simple graph of $ \\ell $ vertices $ \\{1, \\dots, \\ell \\} $ with edge set $ E_{G} $. The graphical arrangement $ \\mathcal{A}_{G} $ consists of hyperplanes $ \\{x_{i}-x_{j}=0\\} $, where $ \\{i, j \\} \\in E_{G} $. It is well known that three properties, chordality of $ G $, supersolvability of $ \\mathcal{A}_{G} $, and freeness of $ \\mathcal{A}_{G} $ are equivalent. Recently, Richard P. Stanley introduced $ \\psi $-graphical arrangement $ \\mathcal{A}_{G, \\psi} $ as a generalization of graphical arrangements. Lili Mu and Stanley characterized the supersolvability of the $ \\psi $-graphical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04853","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"}