{"paper":{"title":"New Lower Bounds for the Number of Pseudoline Arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Adrian Dumitrescu, Ritankar Mandal","submitted_at":"2018-09-10T22:39:07Z","abstract_excerpt":"Arrangements of lines and pseudolines are fundamental objects in discrete and computational geometry. They also appear in other areas of computer science, such as the study of sorting networks. Let $B_n$ be the number of nonisomorphic arrangements of $n$ pseudolines and let $b_n=\\log_2{B_n}$. The problem of estimating $B_n$ was posed by Knuth in 1992. Knuth conjectured that $b_n \\leq {n \\choose 2} + o(n^2)$ and also derived the first upper and lower bounds: $b_n \\leq 0.7924 (n^2 +n)$ and $b_n \\geq n^2/6 -O(n)$. The upper bound underwent several improvements, $b_n \\leq 0.6988\\, n^2$ (Felsner, 1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03619","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"}