{"paper":{"title":"Sharply k-transitive actions on ultrahomogeneous structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GR","authors_text":"J. de la Nuez Gonz\\'alez, Rob Sullivan","submitted_at":"2025-02-16T15:37:28Z","abstract_excerpt":"Given an action of a group $G$ by automorphisms on an infinite relational structure $\\mathcal{M}$, we say that the action is structurally sharply $k$-transitive if, for any two $k$-tuples $\\bar{a}, \\bar{b} \\in M^k$ of distinct elements such that $\\bar{a} \\mapsto \\bar{b}$ is an isomorphism, there exists exactly one element of $G$ sending $\\bar{a}$ to $\\bar{b}$. This generalises the well-known notion of a sharply $k$-transitive action on a set. We show that, for $k \\leq 3$, a wide range of countable ultrahomogeneous structures admit structurally sharply $k$-transitive actions by finitely generat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.11166","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/2502.11166/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"}