Year: 2025
Type: preprint
Abstract: To a homogeneous real bivariate form we associate a family of Toeplitz matrices, as well as a family of auxiliary homogeneous real bivariate forms called higher Hessian polynomials. We show that for a given form, certain positivity properties of its higher Hessian polynomials imply total nonnegativity of its Toeplitz matrices. One of our main result turns out to be equivalent to a special case of a deep theorem from Hodge theory due to E. Cattani. Our other result uses a recent theorem of S. Karp and K. Purbhoo related to problems in real Schubert calculus.
Source: arXiv (Cornell University)
Author: McDaniel, Chris
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416839788
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