{"paper":{"title":"From Aztec diamonds to pyramids: steep tilings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.PR"],"primary_cat":"math.CO","authors_text":"Guillaume Chapuy, J\\'er\\'emie Bouttier, Sylvie Corteel","submitted_at":"2014-07-02T18:05:29Z","abstract_excerpt":"We introduce a family of domino tilings that includes tilings of the Aztec diamond and pyramid partitions as special cases. These tilings live in a strip of $\\mathbb{Z}^2$ of the form $1 \\leq x-y \\leq 2\\ell$ for some integer $\\ell \\geq 1$, and are parametrized by a binary word $w\\in\\{+,-\\}^{2\\ell}$ that encodes some periodicity conditions at infinity. Aztec diamond and pyramid partitions correspond respectively to $w=(+-)^\\ell$ and to the limit case $w=+^\\infty-^\\infty$. For each word $w$ and for different types of boundary conditions, we obtain a nice product formula for the generating functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0665","kind":"arxiv","version":3},"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"}