{"paper":{"title":"Enumeration of symmetric centered rhombus tilings of a hexagon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anisse Kasraoui, Christian Krattenthaler","submitted_at":"2013-06-06T13:19:39Z","abstract_excerpt":"A rhombus tiling of a hexagon is said to be centered if it contains the central lozenge. We compute the number of vertically symmetric rhombus tilings of a hexagon with side lengths $a, b, a, a, b, a$ which are centered. When $a$ is odd and $b$ is even, this shows that the probability that a random vertically symmetric rhombus tiling of a $a, b, a, a, b, a$ hexagon is centered is exactly the same as the probability that a random rhombus tiling of a $a, b, a, a, b, a$ hexagon is centered. This also leads to a factorization theorem for the number of all rhombus tilings of a hexagon which are cen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1403","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"}