{"paper":{"title":"Injectivity of symmetric polynomial maps on partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Katherine Tung, Rohith Thomas","submitted_at":"2026-06-18T04:59:10Z","abstract_excerpt":"Introduced by Ballantine, Beck, and Merca, the elementary symmetric partition function $\\mathrm{pre}_k$, defined on the set of partitions with at least $k$ parts, has been a topic of recent interest. We prove that $\\mathrm{pre}_k$ is injective on the set of $m$-ary partitions for positive integers $m \\ge k$, generalizing the binary $k = 2$ result of Ballantine, Beck, and Merca, and complementing a result of Hadelyn, Niergarth, Li and Li showing that, for each $k \\ge 3$, $\\mathrm{pre}_k$ is not injective on partitions of $n$ with length $2k$ for infinitely many $n$. We introduce the skew Schur "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19796","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/2606.19796/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"}