{"paper":{"title":"Sequence entropy and independence in free and minimal actions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Irma Le\\'on-Torres, Jaime G\\'omez, V\\'ictor Mu\\~noz-L\\'opez","submitted_at":"2025-04-01T16:57:29Z","abstract_excerpt":"For every countable infinite group that admits $\\mathbb{Z}$ as a homomorphic image, we show that for each $m\\in\\mathbb{N}$, there exists a minimal action whose topological sequence entropy is $\\log(m)$. Furthermore, for every countable infinite group $G$ that contains a finite index normal subgroup $G'$ isomorphic to $\\mathbb{Z}^r$, and for every $m\\in \\mathbb{N}$, we found a free minimal action with topological sequence entropy $\\log(n)$, where $m\\leq n\\leq m^{2^r[G:G']}$. In both cases, we also show that the aforementioned minimal actions admit non-trivial independence tuples of size $n$ but"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.00960","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/2504.00960/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"}