{"paper":{"title":"Shuffled equi-n-squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"M. Van de Vel (Vrije Universiteit Amsterdam, Universiteit Antwerpen)","submitted_at":"2017-01-09T19:13:11Z","abstract_excerpt":"A formal n-square is the set of positions in an square matrix of size n. A shuffle of a formal n-square consists of independent rotations of each row and of each column. A key result turns out to be valid at least for n <= 34 and n = 37: Each set of n positions can be mapped with one shuffle onto a transversal of the columns. We consider two applications to equi-n-squares (i.e., n-matrices filled with digits 0, .., n - 1 in equal amounts).\n  First, a shuffled equi-n-square can be seen as a torus with n colors and two orthogonal layers of n rings that can be rotated. Unlike Rubik's cube, each p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02325","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"}