{"paper":{"title":"Counting connected hypergraphs via the probabilistic method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"B\\'ela Bollob\\'as, Oliver Riordan","submitted_at":"2014-04-23T16:52:07Z","abstract_excerpt":"In 1990 Bender, Canfield and McKay gave an asymptotic formula for the number of connected graphs on $[n]$ with $m$ edges, whenever $n$ and the nullity $m-n+1$ tend to infinity. Asymptotic formulae for the number of connected $r$-uniform hypergraphs on $[n]$ with $m$ edges and so nullity $t=(r-1)m-n+1$ were proved by Karo\\'nski and \\L uczak for the case $t=o(\\log n/\\log\\log n)$, and Behrisch, Coja-Oghlan and Kang for $t=\\Theta(n)$. Here we prove such a formula for any $r\\ge 3$ fixed, and any $t=t(n)$ satisfying $t=o(n)$ and $t\\to\\infty$ as $n\\to\\infty$. This leaves open only the (much simpler) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5887","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"}