{"paper":{"title":"Twisted Recurrence via Polynomial Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.DS","authors_text":"Alexander Fish, Kamil Bulinski","submitted_at":"2017-06-24T08:10:31Z","abstract_excerpt":"In this paper we show how polynomial walks can be used to establish a twisted recurrence for sets of positive density in $\\mathbb{Z}^d$. In particular, we prove that if $\\Gamma \\leq \\operatorname{GL}_d(\\mathbb{Z})$ is finitely generated by unipotents and acts irreducibly on $\\mathbb{R}^d$, then for any set $B \\subset \\mathbb{Z}^d$ of positive density, there exists $k \\geq 1$ such that for any $v \\in k \\mathbb{Z}^d$ one can find $\\gamma \\in \\Gamma$ with $\\gamma v \\in B - B$. Our method does not require the linearity of the action, and we prove a twisted recurrence for semigroups of maps from $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07921","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":""},"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"}