{"paper":{"title":"A Sidon-type condition on set systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jane Wodlinger, Peter J. Dukes","submitted_at":"2012-10-02T20:58:55Z","abstract_excerpt":"Consider families of $k$-subsets (or blocks) on a ground set of size $v$. Recall that if all $t$-subsets occur with the same frequency $\\lambda$, one obtains a $t$-design with index $\\lambda$. On the other hand, if all $t$-subsets occur with different frequencies, such a family has been called (by Sarvate and others) a $t$-adesign. An elementary observation shows that such families always exist for $v > k \\ge t$. Here, we study the smallest possible maximum frequency $\\mu=\\mu(t,k,v)$.\n  The exact value of $\\mu$ is noted for $t=1$ and an upper bound (best possible up to a constant multiple) is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0923","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"}