{"paper":{"title":"A Gale-Berlekamp permutation-switching problem in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Marinho Pellegrino, Gustavo Araujo","submitted_at":"2018-01-28T07:49:55Z","abstract_excerpt":"Let an $n\\times n$ array $\\left( a_{ij}\\right) $ of lights be given, each either on (when $a_{ij}=1$) or off (when $a_{ij}=-1$). For each row and each column there is a switch so that if the switch is pulled ($x_{i}=-1$ for row $i$ and $y_{j}=-1$ for column $j$) all of the lights in that line are switched: on to off or off to on. The unbalancing lights problem (Gale-Berlekamp switching game) consists in maximizing the difference between the lights on and off. We obtain the exact parameters for a generalization of the unbalancing lights problem in higher dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09194","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"}