Weiqi Jiang

Type-Voltage Covers and Finite Locally Kneser Graphs

For every integer d ≥ 3, we construct a connected graph on twice the binomial coefficient ‘3d + 1 choose d’ vertices that is locally the Kneser graph K(2d + 1, d). The construction on the line n = 2d + 1 uses a binary voltage cover of K(3d + 1, d), with voltage determined only by...

Bezoutian Decoupling for Conformal Yang–Mills Multiplets in (A)dS

Metsaev's formulation of conformal Yang–Mills theory in six, eight, and ten dimensions admits a change of variables from a generic auxiliary-field presentation to a direct sum of massless and massive Stueckelberg systems. The proposed matrices in arbitrary even dimension were lef...

Prism-Slice h-star Polynomials: Interlacing Through Reduced Level Five and a Level-Six Counterexample

Let c be a positive integer capacity vector with total capacity C, let 1 ≤ k ≤ C − 1, and put m = min{k, C − k}. We prove both clauses of the prism-slice conjecture when m ≤ 5: the h-star polynomial is real-rooted, and for every legal unit split the unsplit polynomial weakly inte...

Prism-Slice h-star Polynomials: Interlacing Through Reduced Level Five and a Level-Six Counterexample

Let c be a positive integer capacity vector with total capacity C, let 1 ≤ k ≤ C − 1, and put m = min{k, C − k}. We prove both clauses of the prism-slice conjecture when m ≤ 5: the h-star polynomial is real-rooted, and for every legal unit split the unsplit polynomial weakly inte...

Exact Signs and Sharp Boundaries for Product-Binomial Dold Coefficients

Let X be a rational exterior space and let f: X → X. Let A = Q(f*) be the graded action on the indecomposable quotient of the positive-degree rational cohomology of X. Suppose that χ_A(t) = t^s ∏_j (t^{n_j} − a_j)^{k_j}, with a nonempty product and every a_j ≥ 3. Powering the bin...

Exact Signs and Sharp Boundaries for Product-Binomial Dold Coefficients

Let X be a rational exterior space and let f: X → X. Let A = Q(f*) be the graded action on the indecomposable quotient of the positive-degree rational cohomology of X. Suppose that χ_A(t) = t^s ∏_j (t^{n_j} − a_j)^{k_j}, with a nonempty product and every a_j ≥ 3. Powering the bin...