{"paper":{"title":"Mixing Properties for Hom-Shifts and the Distance between Walks on Associated Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DS","authors_text":"Brian Marcus, Nishant Chandgotia","submitted_at":"2016-07-28T08:44:29Z","abstract_excerpt":"Let $\\mathcal H$ be a finite connected undirected graph and $\\mathcal H_{walk}$ be the graph of bi-infinite walks on $\\mathcal H$; two such walks $\\{x_i\\}_{i\\in \\mathbb Z}$ and $\\{y_i\\}_{i \\in \\mathbb Z}$ are said to be adjacent if $x_i$ is adjacent to $y_i$ for all $i \\in \\mathbb Z$. We consider the question: Given a graph $\\mathcal H$ when is the diameter (with respect to the graph metric) of $\\mathcal H_{walk}$ finite? Such questions arise while studying mixing properties of hom-shifts (shift spaces which arise as the space of graph homomorphisms from the Cayley graph of $\\mathbb Z^d$ with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08357","kind":"arxiv","version":4},"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"}