{"paper":{"title":"The quasi principal rank characteristic sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shaun M. Fallat, Xavier Mart\\'inez-Rivera","submitted_at":"2017-11-03T02:54:29Z","abstract_excerpt":"A minor of a matrix is quasi-principal if it is a principal or an almost-principal minor. The quasi principal rank characteristic sequence (qpr-sequence) of an $n\\times n$ symmetric matrix is introduced, which is defined as $q_1 q_2 \\cdots q_n$, where $q_k$ is $\\tt A$, $\\tt S$, or $\\tt N$, according as all, some but not all, or none of its quasi-principal minors of order $k$ are nonzero. This sequence extends the principal rank characteristic sequences in the literature, which only depend on the principal minors of the matrix. A necessary condition for the attainability of a qpr-sequence is es"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01003","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"}