{"paper":{"title":"Efficient Uniform Sampling of Surjections via their Profiles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"cs.DS","authors_text":"Arnaud Carayol, Pablo Rotondo","submitted_at":"2026-05-22T08:20:44Z","abstract_excerpt":"In this article, we develop efficient sampling algorithms for random surjections from $[n]$ to $[k]$ for all $n \\geq k$. We make no assumption about $n$ and $k$. In particular, we do not make the common assumption that the ratio $\\frac{n}{k}$ is constant. All our guarantees are uniform in $n$ and $k$.\n  Our first insight is that all the complexity in sampling random surjections is captured by sampling a smaller structure which we call the \\emph{profile} of the surjection. More precisely, the profile associates to each occurring preimage size $s$ the number of preimages of size $s$. Using stand"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24068","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.24068/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}