{"paper":{"title":"The structure of multiplicative tilings of the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mihail N. Kolountzakis, Yang Wang","submitted_at":"2017-10-09T14:12:49Z","abstract_excerpt":"Suppose $\\Omega, A \\subseteq \\RR\\setminus\\Set{0}$ are two sets, both of mixed sign, that $\\Omega$ is Lebesgue measurable and $A$ is a discrete set. We study the problem of when $A \\cdot \\Omega$ is a (multiplicative) tiling of the real line, that is when almost every real number can be uniquely written as a product $a\\cdot \\omega$, with $a \\in A$, $\\omega \\in \\Omega$. We study both the structure of the set of multiples $A$ and the structure of the tile $\\Omega$. We prove strong results in both cases. These results are somewhat analogous to the known results about the structure of translational "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03108","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"}