{"paper":{"title":"Lower bounds for the circuit size of partially homogeneous polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.LO"],"primary_cat":"cs.CC","authors_text":"H\\^ong V\\^an L\\^e","submitted_at":"2013-02-14T10:37:50Z","abstract_excerpt":"In this paper we associate to each multivariate polynomial $f$ that is homogeneous relative to a subset of its variables a series of polynomial families $P_\\lambda (f)$ of $m$-tuples of homogeneous polynomials of equal degree such that the circuit size of any member in $P_\\lambda (f)$ is bounded from above by the circuit size of $f$. This provides a method for obtaining lower bounds for the circuit size of $f$ by proving $(s,r)$-(weak) elusiveness of the polynomial mapping associated with $P_\\lambda (f)$. We discuss some algebraic methods for proving the $(s,r)$-(weak) elusiveness. We also imp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3360","kind":"arxiv","version":6},"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"}