{"paper":{"title":"On the topology of complexes of injective words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ran Levi, Roy Meshulam, Wojtek Chacholski","submitted_at":"2019-08-09T10:07:43Z","abstract_excerpt":"An injective word over a finite alphabet $V$ is a sequence $w=v_1v_2\\cdots v_t$ of distinct elements of $V$. The set $\\mathrm{inj}(V)$ of injective words on $V$ is partially ordered by inclusion. A complex of injective words is the order complex $\\Delta(W)$ of a subposet $W \\subset \\mathrm{inj}(V)$. Complexes of injective words arose recently in applications of algebraic topology to neuroscience, and are of independent interest in topology and combinatorics. In this article we mainly study Permutation Complexes, i.e. complexes of injective words $\\Delta(W)$, where $W$ is the downward closed su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03394","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/1908.03394/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"}