{"paper":{"title":"Baby-Step Giant-Step Algorithms for the Symmetric Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.GR"],"primary_cat":"cs.SC","authors_text":"Bryce Sandlund, Eric Bach","submitted_at":"2016-12-11T19:15:48Z","abstract_excerpt":"We study discrete logarithms in the setting of group actions. Suppose that $G$ is a group that acts on a set $S$. When $r,s \\in S$, a solution $g \\in G$ to $r^g = s$ can be thought of as a kind of logarithm. In this paper, we study the case where $G = S_n$, and develop analogs to the Shanks baby-step / giant-step procedure for ordinary discrete logarithms. Specifically, we compute two sets $A, B \\subseteq S_n$ such that every permutation of $S_n$ can be written as a product $ab$ of elements $a \\in A$ and $b \\in B$. Our deterministic procedure is optimal up to constant factors, in the sense tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03456","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"}