{"paper":{"title":"Improvements on Permutation Reconstruction from Minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Wenjie Zhong, Xiande Zhang, Yiming Ma","submitted_at":"2024-11-19T18:36:53Z","abstract_excerpt":"We study the reconstruction problem of permutation sequences from their $k$-minors, which are subsequences of length $k$ with entries renumbered by $1,2,\\ldots,k$ preserving order. We prove that the minimum number $k$ such that any permutation of length $n$ can be reconstructed from the multiset of its $k$-minors is between $\\exp{(\\Omega(\\sqrt{\\ln n}))}$ and $O(\\sqrt{n\\ln n})$. These results imply better bounds of a well-studied parameter $N_d$, which is the smallest number such that any permutation of length $n\\ge N_d$ can be reconstructed by its $(n-d)$-minors. The new bounds are $ d+\\exp(\\O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12718","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.12718/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}