{"paper":{"title":"Succinct Representations of Permutations and Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"J. Ian Munro, Rajeev Raman, S. Srinivasa Rao, Venkatesh Raman","submitted_at":"2011-08-09T17:01:12Z","abstract_excerpt":"We investigate the problem of succinctly representing an arbitrary permutation, \\pi, on {0,...,n-1} so that \\pi^k(i) can be computed quickly for any i and any (positive or negative) integer power k. A representation taking (1+\\epsilon) n lg n + O(1) bits suffices to compute arbitrary powers in constant time, for any positive constant \\epsilon <= 1. A representation taking the optimal \\ceil{\\lg n!} + o(n) bits can be used to compute arbitrary powers in O(lg n / lg lg n) time.\n  We then consider the more general problem of succinctly representing an arbitrary function, f: [n] \\rightarrow [n] so "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1983","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"}