{"paper":{"title":"Spectra and eigenvectors of the Segre transformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ilse Fischer, Martina Kubitzke","submitted_at":"2013-03-21T18:21:57Z","abstract_excerpt":"Given two sequences $\\fa=(a_n)_{n\\geq 0}$ and $\\fb=(b_n)_{n\\geq 0}$ of complex numbers such that their generating series are of the form $\\sum_{n\\geq 0}a_n t^n=\\frac{\\fh(\\fa)(t)}{(1-t)^{d_{\\fa}}}$ and $\\sum_{n\\geq 0}b_n t^n=\\frac{\\fh(\\fb)(t)}{(1-t)^{d_{\\fb}}}$, where $\\fh(\\fa)(t)$ and $\\fh(\\fb)(t)$ are polynomials, we consider their Segre product $\\fa\\ast\\fb=(a_nb_n)_{n\\geq 0}$. We are interested in the bilinear transformations that compute the coefficient sequence of $\\fh(\\fa\\ast\\fb)(t)$ from those of $\\fh(\\fa)(t)$ and $\\fh(\\fb)(t)$, where $\\sum_{n\\geq 0}a_nb_n t^n=\\frac{\\fh(\\fa\\ast\\fb)(t)}{("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5358","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"}