{"paper":{"title":"Classification of Ding's Schubert varieties: finer rook equivalence","license":"","headline":"","cross_cats":["math.CO","math.GT"],"primary_cat":"math.AG","authors_text":"Jeremy L. Martin, Mike Develin, Victor Reiner","submitted_at":"2004-03-31T19:13:31Z","abstract_excerpt":"K. Ding studied a class of Schubert varieties X_\\lambda in type A partial flag manifolds, corresponding to integer partitions \\lambda and in bijection with dominant permutations. He observed that the Schubert cell structure of X_\\lambda is indexed by maximal rook placements on the Ferrers board B_\\lambda, and that the integral cohomology groups H^*(X_\\lambda; Zz), H^*(X_\\mu; Zz) are additively isomorphic exactly when the Ferrers boards B_\\lambda, B_\\mu satisfy the combinatorial condition of rook-equivalence.\n  We classify the varieties X_\\lambda up to isomorphism, distinguishing them by their "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0403530","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}