{"paper":{"title":"$\\mathcal{P}$-schemes and Deterministic Polynomial Factoring over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.GR","math.NT"],"primary_cat":"cs.CC","authors_text":"Zeyu Guo","submitted_at":"2017-06-30T05:42:59Z","abstract_excerpt":"We introduce a family of mathematical objects called $\\mathcal{P}$-schemes, where $\\mathcal{P}$ is a poset of subgroups of a finite group $G$. A $\\mathcal{P}$-scheme is a collection of partitions of the right coset spaces $H\\backslash G$, indexed by $H\\in\\mathcal{P}$, that satisfies a list of axioms. These objects generalize the classical notion of association schemes as well as the notion of $m$-schemes (Ivanyos et al. 2009).\n  Based on $\\mathcal{P}$-schemes, we develop a unifying framework for the problem of deterministic factoring of univariate polynomials over finite fields under the gener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10028","kind":"arxiv","version":2},"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"}