{"paper":{"title":"Kernelization lower bound for Permutation Pattern Matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Ivan Bliznets, Lukas Mach, Marek Cygan, Pawel Komosa","submitted_at":"2014-06-04T19:32:04Z","abstract_excerpt":"A permutation $\\pi$ contains a permutation $\\sigma$ as a pattern if it contains a subsequence of length $|\\sigma|$ whose elements are in the same relative order as in the permutation $\\sigma$. This notion plays a major role in enumerative combinatorics. We prove that the problem does not have a polynomial kernel (under the widely believed complexity assumption $\\mbox{NP} \\not\\subseteq \\mbox{co-NP}/\\mbox{poly}$) by introducing a new polynomial reduction from the clique problem to permutation pattern matching."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1158","kind":"arxiv","version":2},"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"}