{"paper":{"title":"The Relation between Composability and Splittability of Permutation Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rachel Zhang","submitted_at":"2019-08-07T17:06:02Z","abstract_excerpt":"A permutation class $C$ is said to be splittable if there exist two proper subclasses $A, B \\subsetneq C$ such that any $\\sigma \\in C$ can be red-blue colored so that the red (respectively, blue) subsequence of $\\sigma$ is order isomorphic to an element of $A$ (respectively, $B$). The class $C$ is said to be composable if there exists some number of proper subclasses $A_1, \\dots, A_k \\subsetneq C$ such that any $\\sigma \\in C$ can be written as $\\alpha_1 \\circ \\dots \\circ \\alpha_k$ for some $\\alpha_i \\in A_i$. We answer a question of Karpilovskij by showing that there exists a composable permut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02731","kind":"arxiv","version":3},"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/1908.02731/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"}