{"paper":{"title":"Critical groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields: an extended abstract","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RA"],"primary_cat":"math.CO","authors_text":"Dmitrii V. Pasechnik, Henk D. L. Hollmann, Swee Hong Chan","submitted_at":"2013-12-07T16:58:50Z","abstract_excerpt":"We determine the critical groups of the generalized de Bruijn graphs DB$(n,d)$ and generalized Kautz graphs Kautz$(n,d)$, thus extending and completing earlier results for the classical de Bruijn and Kautz graphs. Moreover, for a prime $p$ the critical groups of DB$(n,p)$ are shown to be in close correspondence with groups of $n\\times n$ circulant matrices over $\\mathbb{F}_p$, which explains numerical data in [OEIS:A027362], and suggests the possibility to construct normal bases in $\\mathbb{F}_{p^n}$ from spanning trees in DB$(n,p)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2114","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"}