{"paper":{"title":"Combinatorial identities related to $2\\times 2$ submatrices of recursive matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arthur L.B. Yang, Fangfang Cai, Qing-Hu Hou, Yidong Sun","submitted_at":"2018-08-17T03:05:53Z","abstract_excerpt":"Recursive matrices are ubiquitous in combinatorics, which have been extensively studied. We focus on the study of the sums of $2\\times 2$ minors of certain recursive matrices, the alternating sums of their $2\\times 2$ minors, and the sums of their $2\\times 2$ permanents. We obtain some combinatorial identities related to these sums, which generalized the work of Sun and Ma in [{\\it Electron. J. Combin. 2014}] and [{\\it European J. Combin. 2014}]. With the help of the computer algebra package {\\tt HolonomicFunctions}, we further get some new identities involving Narayana polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05736","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"}