{"paper":{"title":"Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carla D. Savage, Megan A. Martinez","submitted_at":"2016-09-26T18:19:28Z","abstract_excerpt":"Inversion sequences of length $n$, $\\mathbf{I}_n$, are integer sequences $(e_1, \\ldots, e_n)$ with $0 \\leq e_i < n$ for each $i$. The study of patterns in inversion sequences was initiated recently by Mansour-Shattuck and Corteel-Martinez-Savage-Weselcouch through a systematic study of inversion sequences avoiding words of length 3. We continue this investigation by generalizing the notion of a pattern to a fixed triple of binary relations $(\\rho_1,\\rho_2,\\rho_3)$ and consider the set $\\mathbf{I}_n(\\rho_1,\\rho_2,\\rho_3)$ consisting of those $e \\in \\mathbf{I}_n$ with no $i < j < k$ such that $e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08106","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"}