{"paper":{"title":"The number of multiplicative Sidon sets of integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Hong Liu, P\\'eter P\\'al Pach","submitted_at":"2018-08-19T08:05:43Z","abstract_excerpt":"A set $S$ of natural numbers is multiplicative Sidon if the products of all pairs in $S$ are distinct. Erd\\H{o}s in 1938 studied the maximum size of a multiplicative Sidon subset of $\\{1,\\ldots, n\\}$, which was later determined up to the lower order term: $\\pi(n)+\\Theta(\\frac{n^{3/4}}{(\\log n)^{3/2}})$. We show that the number of multiplicative Sidon subsets of $\\{1,\\ldots, n\\}$ is $T(n)\\cdot 2^{\\Theta(\\frac{n^{3/4}}{(\\log n)^{3/2}})}$ for a certain function $T(n)\\approx 2^{1.815\\pi(n)}$ which we specify. This is a rare example in which the order of magnitude of the lower order term in the exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06182","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"}