{"paper":{"title":"Which Exterior Powers are Balanced?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abigail Raz, Christino Tamon, Devlin Mallory, Thomas Zaslavsky","submitted_at":"2013-01-06T04:23:48Z","abstract_excerpt":"A signed graph is a graph whose edges are given (-1,+1) weights. In such a graph, the sign of a cycle is the product of the signs of its edges. A signed graph is called balanced if its adjacency matrix is similar to the adjacency matrix of an unsigned graph via conjugation by a diagonal (-1,+1) matrix. For a signed graph $\\Sigma$ on n vertices, its exterior k-th power, where k=1,..,n-1, is a graph $\\bigwedge^{k} \\Sigma$ whose adjacency matrix is given by \\[ A({$\\bigwedge^{k} {\\Sigma}$}) = P^{\\dagger} A(\\Sigma^{\\Box k}) P, \\] where P is the projector onto the anti-symmetric subspace of the k-fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0973","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"}