{"paper":{"title":"Maximal independent sets in the middle two layers of the Boolean lattice","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ce Chen, J\\'ozsef Balogh, Ramon I. Garcia","submitted_at":"2025-04-30T19:00:31Z","abstract_excerpt":"Let $B(2d-1, d)$ be the subgraph of the hypercube $\\mathcal{Q}_{2d-1}$ induced by its two largest layers. Duffus, Frankl and R\\\"odl proposed the problem of finding the asymptotics for the logarithm of the number of maximal independent sets in $B(2d-1, d)$. Ilinca and Kahn determined the logarithmic asymptotics and reiterated the question of what their order of magnitude is. We show that the number of maximal independent sets in $B(2d-1,d)$ is \\[ \\left(1+o(1)\\right)(2d-1)\\exp\\left(\\frac{(d-1)^2}{2^{2d-1}}\\binom{2d-2}{d-1}\\right)\\cdot 2^{\\binom{2d-2}{d-1}}, \\] and describe their typical structur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00132","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.00132/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}