{"paper":{"title":"Waring Rank, Parameterized and Exact Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Kevin Pratt","submitted_at":"2018-07-17T03:17:27Z","abstract_excerpt":"Given nonnegative integers $n$ and $d$, where $n \\gg d$, what is the minimum number $r$ such that there exist linear forms $\\ell_1, \\ldots, \\ell_r \\in \\mathbb{C}[x_1, \\ldots, x_n]$ so that $\\ell_1^d + \\cdots + \\ell_r^d$ is supported exactly on the set of all degree-$d$ multilinear monomials in $x_1, \\ldots, x_n$? We show that this and related questions have surprising and intimate connections to the areas of parameterized and exact algorithms, generalizing several well-known methods and providing a concrete approach to obtain faster approximate counting and deterministic decision algorithms. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06194","kind":"arxiv","version":4},"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"}