{"paper":{"title":"Spin models and distance-regular graphs of $q$-Racah type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CO","authors_text":"Kazumasa Nomura, Paul Terwilliger","submitted_at":"2023-08-21T22:11:08Z","abstract_excerpt":"Let $\\Gamma$ denote a distance-regular graph, with vertex set $X$ and diameter $D\\geq 3$. We assume that $\\Gamma$ is formally self-dual and $q$-Racah type. We also assume that for each $x \\in X$ the subconstituent algebra $T=T(x)$ contains a certain central element $Z=Z(x)$. We use $Z$ to construct a spin model $\\sf W$ afforded by $\\Gamma$. We investigate the combinatorial implications of $Z$. We reverse the logical direction and recover $Z$ from $\\sf W$. We finish with some open problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.11061","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/2308.11061/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"}