Ryu Ogawa

Petal rigidity and access forcing in polynomial lemniscates: an exponent-sharp rigidity threshold for a path problem of Erdős, Herzog, and Piranian

Let f be a monic polynomial of degree n ≥ 2 whose roots all lie in the open unit disk, let Λ = {z : |f(z)| < 1}, let c = |f(0)|, and let β = Σ_j |ζ_j| be the ℓ¹-mass of the critical points of f. Erdős, Herzog, and Piranian proved that some connected component of Λ contains at lea...

Petal rigidity and access forcing in polynomial lemniscates: an exponent-sharp rigidity threshold for a path problem of Erdős, Herzog, and Piranian

Let f be a monic polynomial of degree n ≥ 2 whose roots all lie in the open unit disk, let Λ = {z : |f(z)| < 1}, let c = |f(0)|, and let β = Σ_j |ζ_j| be the ℓ¹-mass of the critical points of f. Erdős, Herzog, and Piranian proved that some connected component of Λ contains at lea...

Separated sumsets: upper bounds for B_{3,Δ}- and B_{4,Δ}-sets of real numbers

Call a finite set S of real numbers a 1-separated B_h set if any two distinct h-element multisets from S have sums differing by at least 1. These are the real, unit-separation cases of the B_{h,Δ}-sets recently introduced by Nathanson. We prove that a 1-separated B₃ set S ⊆ [0,V]...