{"paper":{"title":"Interlacing properties and the Schur-Szeg\\H{o} composition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Vladimir Petrov Kostov","submitted_at":"2015-04-09T14:13:18Z","abstract_excerpt":"Each degree $n$ polynomial in one variable of the form $(x+1)(x^{n-1}+c_1x^{n-2}+\\cdots +c_{n-1})$ is representable in a unique way as a Schur-Szeg\\H{o} composition of $n-1$ polynomials of the form $(x+1)^{n-1}(x+a_i)$, see \\cite{Ko1}, \\cite{AlKo} and \\cite{Ko2}. Set $\\sigma _j:=\\sum _{1\\leq i_1<\\cdots <i_j\\leq n-1}a_{i_1}\\cdots a_{i_j}$. The eigenvalues of the affine mapping $(c_1,\\ldots ,c_{n-1})\\mapsto (\\sigma _1,\\ldots ,\\sigma _{n-1})$ are positive rational numbers and its eigenvectors are defined by hyperbolic polynomials (i.e. with real roots only). In the present paper we prove interlac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02321","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}