{"paper":{"title":"Criteria of valid line sum arrays for multidimensional matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hyun Kwang Kim, Joon Yop Lee","submitted_at":"2013-04-29T00:29:51Z","abstract_excerpt":"Gale and Ryser found a criterion for existence of a binary matrix with given row and column sums. Mirsky extended the theorem of Gale and Ryser to $q$-ary matrices. In this paper, we are interested in higher dimensional extension of these theorems. We first introduce multidimensional matrices as a higher dimensional generalization of matrices. We next replace the concept of row and columns in matrices by lines in multidimensional matrices. We finally find a criterion for existence of a $q$-ary multidimensional matrices with given line sums."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7543","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"}