{
  "annotation_id": "71637d82-b7f0-4518-a574-3815a0e96751",
  "date_created": "2026-02-17T05:53:24.265000Z",
  "date_modified": "2026-02-17T05:53:24.265000Z",
  "file_hash": "9cd8b83cff0abec40028a9d114a30e908a4403e1d6d25cfef65fa1bbccb9e022",
  "private": false,
  "record": {
    "abstract": "We establish a Schur--Horn type inequality for symmetric hyperbolic polynomials. As an immediate consequence, we resolve a conjecture of Nam Q. Le on Hadamard-type inequalities for hyperbolic polynomials. Our argument is based on the Schur--Horn theorem, the Birkhoff theorem, and G{\\aa}rding\u0027s concavity theorem for hyperbolicity cones. Beyond the eigenvalue level, we develop a symmetrization principle on hyperbolicity cones: if a hyperbolic polynomial is invariant under a finite group action, then its value increases under the associated Reynolds operator (group averaging). Applied to the sign-flip symmetries of linear principal minor polynomials introduced by Blekherman et al., this yields a short proof of the hyperbolic Fischer--Hadamard inequalities for PSD-stable lpm polynomials.",
    "arxiv_id": "2601.10602",
    "authors": [
      "Teng Zhang"
    ],
    "categories": [
      "math.FA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Schur--Horn type inequalities for hyperbolic polynomials",
    "url": "https://arxiv.org/abs/2601.10602",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "16018e36-9472-43bc-87a0-1822a9666378",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}