{"paper":{"title":"Vanishing ideals of Lattice Diagram determinants","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"J.-C. Aval, N. Bergeron","submitted_at":"2001-07-21T00:08:41Z","abstract_excerpt":"A lattice diagram is a finite set $L=\\{(p_1,q_1),... ,(p_n,q_n)\\}$ of lattice cells in the positive quadrant. The corresponding lattice diagram determinant is $\\Delta_L(\\X;\\Y)=\\det \\| x_i^{p_j}y_i^{q_j} \\|$. The space $M_L$ is the space spanned by all partial derivatives of $\\Delta_L(\\X;\\Y)$. We denote by $M_L^0$ the $Y$-free component of $M_L$. For $\\mu$ a partition of $n+1$, we denote by $\\mu/ij$ the diagram obtained by removing the cell $(i,j)$ from the Ferrers diagram of $\\mu$. Using homogeneous partially symmetric polynomials, we give here a dual description of the vanishing ideal of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107155","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"}