{"paper":{"title":"Geometric Reductions of ABS equations on an $n$-cube to discrete Painlev\\'e systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Nalini Joshi, Nobutaka Nakazono, Yang Shi","submitted_at":"2014-02-25T08:30:15Z","abstract_excerpt":"In this paper, we show how to relate $n$-dimensional cubes on which ABS equations hold to the symmetry groups of discrete Painlev\\'e equations. We here focus on the reduction from the 4-dimensional cube to the $q$-discrete third Painlev\\'e equation, which is a dynamical system on a rational surface of type $A_5^{(1)}$ with the extended affine Weyl group $\\widetilde{\\mathcal W}\\bigl((A_2+A_1)^{(1)}\\bigr)$. We provide general theorems to show that this reduction also extends to other discrete Painlev\\'e equations at least of type A."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6084","kind":"arxiv","version":4},"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"}