Gröbner bases and Stanley decompositions of determinantal rings
Copyright policy )Gröbner bases and Stanley decompositions of determinantal rings
Using methods from algebraic combinatorics, we prove that the set of \((r+1)\times (r+1)\)-minors of a generic \(m\times n\)-matrix forms a reduced Gröbner basis (for certain term orders). This yields an efficient normal form algorithm and an explicit Stanley decomposition for the coordinate ring of matrices with rank \(\leq r\).
- DigiZeitschriften Germany
- Cornell University United States
normal form algorithm, Stanley decomposition for the coordinate ring, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, Determinantal varieties, Article, Polynomial rings and ideals; rings of integer-valued polynomials, 510.mathematics, determinantal ideals, Linkage, complete intersections and determinantal ideals, reduced Gröbner basis
normal form algorithm, Stanley decomposition for the coordinate ring, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic computation and algebraic computation, Determinantal varieties, Article, Polynomial rings and ideals; rings of integer-valued polynomials, 510.mathematics, determinantal ideals, Linkage, complete intersections and determinantal ideals, reduced Gröbner basis
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