{"paper":{"title":"Random Latin squares and 2-dimensional expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Lubotzky, Roy Meshulam","submitted_at":"2013-07-12T21:23:27Z","abstract_excerpt":"Let X be a 2-dimensional simplicial complex. The degree of an edge e is the number of 2-faces of X containing e. The complex X is an \\epsilon-expander if the coboundary d_1(\\phi) of every Z_2-valued 1-cochain \\phi \\in C^1(X;Z_2) satisfies |support(d_1(\\phi))| \\geq \\epsilon |\\supp(\\phi+d_0(\\psi))| for some 0-cochain \\psi. Using a new model of random 2-complexes we show the existence of an infinite family of 2-dimensional \\epsilon-expanders with maximum edge degree d, for some fixed \\epsilon>0 and d."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3582","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"}