{"paper":{"title":"Counting spanning trees of the hypercube and its $q$-analogs by explicit block diagonalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Murali K. Srinivasan","submitted_at":"2011-04-08T05:01:16Z","abstract_excerpt":"The number of spanning trees of a graph $G$ is called the {\\em complexity} of $G$ and is denoted $c(G)$. Let C(n) denote the {\\em (binary) hypercube} of dimension $n$. A classical result in enumerative combinatorics (based on explicit diagonalization) states that $c(C(n)) = \\prod_{k=2}^n (2k)^{n\\choose k}$.\n  In this paper we use the explicit block diagonalization methodology to derive formulas for the complexity of two $q$-analogs of C(n), the {\\em nonbinary hypercube} $\\Cq(n)$, defined for $q\\geq 2$, and the {\\em vector space analog of the hypercube} $\\Cfq(n)$, defined for prime powers $q$.\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1481","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"}