{"paper":{"title":"On the number of lambda terms with prescribed size of their De Bruijn representation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","cs.LO","math.LO"],"primary_cat":"math.CO","authors_text":"Bernhard Gittenberger, Zbigniew Go{\\l}\\k{e}biewski","submitted_at":"2015-09-21T08:23:01Z","abstract_excerpt":"John Tromp introduced the so-called 'binary lambda calculus' as a way to encode lambda terms in terms of binary words. Later, Grygiel and Lescanne conjectured that the number of binary lambda terms with $m$ free indices and of size $n$ (encoded as binary words of length $n$) is $o(n^{-3/2} \\tau^{-n})$ for $\\tau \\approx 1.963448\\ldots$. We generalize the proposed notion of size and show that for several classes of lambda terms, including binary lambda terms with $m$ free indices, the number of terms of size $n$ is $\\Theta(n^{-3/2} \\rho^{-n})$ with some class dependent constant $\\rho$, which in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06139","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"}