{"paper":{"title":"Powers of the Vandermonde determinant are eventually non-SNP","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Melanie Weber, Thien Le","submitted_at":"2026-07-26T20:26:54Z","abstract_excerpt":"We prove a conjecture of Monical, Tokcan, and Yong that every fixed positive power of the Vandermonde determinant is non-SNP in all sufficiently many variables, where a polynomial is non-SNP if there is a lattice point in its Newton polytope that does not appear with nonzero coefficient. This means our result proves that for every even power $k\\geq4$, there is always such a missing lattice monomial in large enough dimensions. The odd case follows from alternation, and the quadratic case was previously known. For every even power $k\\geq4$, we exhibit an explicit lattice point in the Newton poly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23828","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/2607.23828/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"}