{"paper":{"title":"Lattice Diagram Polynomials and Extended Pieri Rules","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CO","authors_text":"A. M. Garsia, F. Bergeron, G. Tesler, M. Haiman, N. Bergeron","submitted_at":"1998-09-22T16:29:06Z","abstract_excerpt":"The lattice cell in the ${i+1}^{st}$ row and ${j+1}^{st}$ column of the positive quadrant of the plane is denoted $(i,j)$. If $\\mu$ is a partition of $n+1$, we denote by $\\mu/ij$ the diagram obtained by removing the cell $(i,j)$ from the (French) Ferrers diagram of $\\mu$. We set $\\Delta_{\\mu/ij}=\\det \\| x_i^{p_j}y_i^{q_j} \\|_{i,j=1}^n$, where $(p_1,q_1),... ,(p_n,q_n)$ are the cells of $\\mu/ij$, and let ${\\bf M}_{\\mu/ij}$ be the linear span of the partial derivatives of $\\Delta_{\\mu/ij}$. The bihomogeneity of $\\Delta_{\\mu/ij}$ and its alternating nature under the diagonal action of $S_n$ gives"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9809126","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":""},"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"}