{"paper":{"title":"A problem of Andrews and Dhar on partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jujian Zhang, Ken Ono, Simon Mahns","submitted_at":"2026-06-03T17:22:10Z","abstract_excerpt":"This paper is motivated by a broad question about AI-assisted mathematics: can an AI system help discover and certify an explicit bijection between two infinite sequences of complicated combinatorial sets already known to be equinumerous? The challenge is to find a reversible structure explaining that equality uniformly across the sequence. We give an affirmative test case in the setting of a partition problem. Andrews and Dhar introduced two partition families $\\mathcal{C}_3(n)$ and $\\mathcal{D}_3(n)$, and for \"nonexceptional'' $n$, they asked for a bijective proof of their equality\n  \\[\n  |\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05117","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/2606.05117/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"}