A Dittert-like inequality for homogeneous stable polynomials
Year: 2026
Type: preprint
Abstract: We prove a coefficient inequality for every homogeneous real stable polynomial P(s, x1, …, xn) of degree n ≥ 1 with nonnegative coefficients. If P(1, 0, …, 0) = 1, ri = ∂xiP(1, 0, …, 0), and ∑i ri = n, the following inequality holds, where brackets denote coefficient extraction: [x1⋯xn] P(0, x1, …, xn) + 2 − ∏i ri − P(0, 1, …, 1) ≥ n!/nn. Equality holds exactly for P = (s + ∑i xi/n)n. The normalizations can be removed by rescaling P and the xi. We give applications to permanents, mixed discriminants, subpermanents, and stable combinatorial measures. In particular, the theorem gives an independent proof of Dittert’s conjecture for nonnegative matrices in every dimension.
Author: Lavi, Yair
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224469707