{"paper":{"title":"A Shifted $t$-Schur Weight from the Modified Odd Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"S.-J. Lee","submitted_at":"2026-07-02T08:03:41Z","abstract_excerpt":"We study the one-time weight on strict partitions obtained from the modified odd Greaves--Jing--Zhu operator. The shifted $t$-Schur functions generated by this operator are obtained from the classical Schur $Q$-functions by the plethystic substitution $X\\mapsto X-tX$. Thus the corresponding weight \\[\n  \\lambda \\longmapsto \\mathcal Q_\\lambda(X;t)P_\\lambda(Y) \\] is a shifted Schur weight with a virtual first alphabet. We give its normalization, its Pfaffian correlation kernel, its Fredholm Pfaffian for the largest part, and its size cumulants. For $t=-q$ with $q\\geq 0$ the virtual alphabet becom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01839","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/2607.01839/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"}