Qihang Wang

Positive formulas for q-Zeta numerators of Ferrers-cell posets

We establish explicit positive formulas for Chapoton's q-Zeta numerators of Ferrers-cell posets F_b = {(i,c): 1 <= i <= r, i <= c <= b_i}, for every integer r >= 1 and every boundary sequence b_1 >= ... >= b_r >= r, together with formulas for every interval of their minimum-augme...

Four Special Directions in AG(2,13): The 52-Point Obstruction and the Sharp Minimum

We prove that no 52-point subset of the affine plane over the field with 13 elements has exactly four special directions, where a direction is special when its thirteen parallel affine lines do not all meet the set in the same number of points. A universal incidence identity and...

Exact Measurement-Dependence Cost across the Noisy GHZ–Mermin Threshold

We determine the exact measurement-dependence cost of faithful local deterministic models reproducing the full outcome table on the even-parity GHZ–Mermin setting set for Pauli X/Y measurements. For every integer n ≥ 3 and isotropic visibility 0 ≤ v ≤ 1, let R = 2^floor((n−1)/2)....

Exact Chained-Word Threshold and Monotone-Path Structure in the Even Root-of-Unity Kaleidoscope Yang–Baxter Algebra

We prove the chained-word vanishing conjecture of Qiu, Guan, and Yu in the even root-of-unity Kaleidoscope Yang–Baxter representation. For every even N ≥ 4, every complex parameter u with u ≠ 0 and u^N ≠ 1, and every integer exponent tuple, the exact universal vanishing threshold...

Cyclic steepest descent is R-superlinearly convergent for almost every initialization on two-spectrum quadratics

We completely classify cyclic steepest descent (CSD) on strictly convex quadratics whose Hessian has exactly two distinct eigenvalues. At the beginning of each cycle CSD recomputes an exact steepest-descent stepsize and reuses it for m updates. For every m >= 2, write A = aP + bQ...

Cyclic steepest descent is R-superlinearly convergent for almost every initialization on two-spectrum quadratics

We completely classify cyclic steepest descent (CSD) on strictly convex quadratics whose Hessian has exactly two distinct eigenvalues. At the beginning of each cycle CSD recomputes an exact steepest-descent stepsize and reuses it for m updates. For every m >= 2, write A = aP + bQ...

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 proves t...

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 proves t...

A counterexample to R-superlinear convergence of cyclic steepest descent

Cyclic steepest descent recomputes an exact steepest-descent stepsize once per cycle and reuses it for m updates. Dai's ICM 2022 survey states that this method is likely to converge R-superlinearly on n-dimensional convex quadratics when m is at least (n+1)/2. We show that the co...

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...

Edge-resolved shifts and abelian rigidity in cores of cubelike graphs

We study cores of cubelike graphs through edge-resolved shifts. We prove three linked structural results. First, every prescribed edge of a core of a cubelike graph is reversed by a shift that maps every vertex to a neighbour. Second, for a connected normal Cayley graph on a fini...

Charge transport, not interaction range, bounds the Lieb-Schultz-Mattis twist cost

Geometric interaction range can overestimate the energy cost of a Lieb-Schultz-Mattis twist. We prove that, under the stated assumptions, every sufficiently large admitted periodic ring with L>3R has an explicit O(1/L) upper bound on its full spectral gap. The bound is governed b...

A Ballot-Word Formula for q-Zeta Numerators of Type-B Root Posets

We determine the Chapoton q-Zeta numerator for the full positive-root poset of standard Lie type B_r, graded by root height minus one and normalized with Chapoton's fixed denominator convention. For every standard Lie rank r >= 1, we identify the root poset with a trapezoidal cel...

A Local Block Criterion for Periodic Morse Reductions of Circulant Independence Complexes

For G_n = Cay(Z/nZ, {±2, ±3}), we determine the homotopy type of its independence complex for every n ≥ 6. If n = 8q + r, the answer is a wedge of five (2q − 1)-spheres for r = 0, one (2q − 1)-sphere for r = 1, 2, 3, three 2q-spheres for r = 4, and one (2q + 1)-sphere for r = 5,...

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...