{"paper":{"title":"Proof of Blum's conjecture on hexagonal dungeons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mihai Ciucu, Tri Lai","submitted_at":"2014-02-28T14:30:02Z","abstract_excerpt":"Matt Blum conjectured that the number of tilings of the Hexagonal Dungeon of sides $a,\\ 2a,\\ b,\\ a,\\ 2a,\\ b$ (where $b\\geq 2a$) is $13^{2a^2}14^{\\lfloor\\frac{a^2}{2}\\rfloor}$ (J. Propp, New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999). In this paper we present a proof for this conjecture using Kuo's Graphical Condensation Theorem (E. Kuo, Applications of Graphical Condensation for Enumerating Matchings and Tilings, Theoretical Computer Science, 2004)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7257","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"}