Gröbner bases and Stanley decompositions of determinantal ideals (Q1825907)

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 \(\leq r\).