{"paper":{"title":"Lamplighter groups, de Bruijn graphs, spider-web graphs and their spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.GR","math.MP"],"primary_cat":"math.CO","authors_text":"Paul-Henry Leemann, Rostislav Grigorchuk, Tatiana Nagnibeda","submitted_at":"2015-02-24T09:20:54Z","abstract_excerpt":"We describe the infinite family of spider-web graphs $S_{k,M,N }$, $k \\geq 2$, $M \\geq 1$ and $N \\geq 0$, studied in physical literature as tensor products of well-known de Brujin graphs $B_{k,N}$ and cyclic graphs $C_M$ and show that these graphs are Schreier graphs of the lamplighter groups $L_k = Z/kZ \\wr Z$. This allows us to compute their spectra and to identify the infinite limit of $S_{k,M,N}$, as $N, M \\to\\infty$, with the Cayley graph of the lamplighter group $L_k$.\n  This is the final version of the article, taking in account comments from the referees and with an extended introducti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06722","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"}