{"paper":{"title":"Spectral expansion of random sum complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Orr Beit-Aharon, Roy Meshulam","submitted_at":"2018-01-19T15:39:59Z","abstract_excerpt":"Let $G$ be a finite abelian group of order $n$ and let $\\Delta_{n-1}$ denote the $(n-1)$-simplex on the vertex set $G$. The sum complex $X_{A,k}$ associated to a subset $A \\subset G$ and $k < n$, is the $k$-dimensional simplicial complex obtained by taking the full $(k-1)$-skeleton of $\\Delta_{n-1}$ together with all $(k+1)$-subsets $\\sigma \\subset G$ that satisfy $\\sum_{x \\in \\sigma} x \\in A$. Let $C^{k-1}(X_{A,k})$ denote the space of complex valued $(k-1)$-cochains of $X_{A,k}$. Let $L_{k-1}:C^{k-1}(X_{A,k}) \\rightarrow C^{k-1}(X_{A,k})$ denote the reduced $(k-1)$-th Laplacian of $X_{A,k}$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06466","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"}