{"paper":{"title":"Avoiding two consecutive blocks of same size and same sum over $\\mathbb{Z}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.FL"],"primary_cat":"math.CO","authors_text":"Matthieu Rosenfeld, Micha\\\"el Rao","submitted_at":"2015-11-18T16:57:08Z","abstract_excerpt":"A long standing question asks whether $\\mathbb{Z}$ is uniformly 2-repetitive [Justin 1972, Pirillo and Varricchio, 1994], that is, whether there is an infinite sequence over a finite subset of $\\mathbb{Z}$ avoiding two consecutive blocks of same size and same sum or not. Cassaigne \\emph{et al.} [2014] showed that $\\mathbb{Z}$ is not uniformly 3-repetitive. We show that $\\mathbb{Z}^2$ is not uniformly 2-repetitive. Moreover, this problem is related to a question from M\\\"akel\\\"a in combinatorics on words and we answer to a weak version of it."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05875","kind":"arxiv","version":2},"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"}