{"paper":{"title":"Relating multiway discrepancy and singular values of graphs and contingency tables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marianna Bolla","submitted_at":"2014-08-27T15:47:27Z","abstract_excerpt":"The $k$-way discrepancy $\\disc_k (\\C)$ of a rectangular array $\\C$ of nonnegative entries is the minimum of the maxima of the within- and between-cluster discrepancies that can be obtained by simultaneous $k$-clusterings (proper partitions) of its rows and columns. In the main theorem, irrespective of the size of $\\C$, we give the following estimate for the $k$th largest non-trivial singular value of the normalized table: $s_k \\le 9\\disc_{k } (\\C ) (k+2 -9k\\ln \\disc_{k } (\\C ))$, provided $\\disc_{k } (\\C ) <1$ and $k\\le \\rk (\\C )$. This statement is the converse of Theorem 7 of Bolla \\cite{Bol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6443","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"}