Dongming Zhang

Fröberg's Conjecture for Quintics and Septics in Four Variables

Let k be a field of characteristic zero and let S = k[x_1,x_2,x_3,x_4]. We prove Fröberg's predicted Hilbert series for ideals generated by r general forms of equal degree d for every r ≥ 1 in each of the two cases d = 5 and d = 7. Relative to the classical cases r ≤ 5 and the eq...

Compatibility Restores Spin Alignment for Three Qubits

We study a spectral majorization problem for lifted quantum marginals. For every three-qubit state, every single-qubit replacement state, arbitrary nonnegative weights on all eight supports, and compatible marginals arising from one global state, we prove that the weighted margin...

Fröberg's Conjecture for Quintics and Septics in Four Variables

Let k be a field of characteristic zero and let S = k[x_1,x_2,x_3,x_4]. We prove Fröberg's predicted Hilbert series for ideals generated by r general forms of equal degree d for every r ≥ 1 in each of the two cases d = 5 and d = 7. Relative to the classical cases r ≤ 5 and the eq...

Hyperplane graph models for cotangent cohomology and quadratic obstructions of matroids

Let $M$ be a finite matroid and let $T^i(M)$ denote the cotangent cohomology of its Stanley--Reisner ring over a field. The paper gives a uniform hyperplane-graph model for every multigraded component of $T^2(M)$ and derives a characteristic-independent fine Hilbert series. It pr...