{"paper":{"title":"Bounded-Support Additive Latin Transversals via Color-Counted Matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Antoine Deza, Sebastian Pokutta, Yan Gerard, Yijun Ma","submitted_at":"2026-07-13T08:27:22Z","abstract_excerpt":"We consider the following additive Latin transversal problem. Given a multiset $A=(a_1,\\dots,a_k)$ of elements of $\\mathbb Z_m$ and a set $B\\subseteq\\mathbb Z_m$ of cardinality $k$, the task is to order $B$ as $b_1,\\dots,b_k$ so that the sums $a_i+b_i$ are pairwise distinct. When $k=m$, Hall proved that a solution exists if and only if $\\sum_{i=1}^m a_i\\equiv 0 \\pmod m$; moreover, his theorem yields a polynomial-time construction. Alon proved that a solution always exists when $m$ is prime and $k<m$, but no polynomial-time construction is known in general. Our main algorithmic contribution is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11241","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/2607.11241/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"}