{"paper":{"title":"Spanning Trees and Mahler Measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Daniel S. Silver, Susan G. Williams","submitted_at":"2016-02-08T21:39:20Z","abstract_excerpt":"The complexity of a finite connected graph is its number of spanning trees; for a non-connected graph it is the product of complexities of its connected components. If $G$ is an infinite graph with cofinite free ${\\mathbb Z}^d$-symmetry, then the logarithmic Mahler measure $m(\\Delta)$ of its Laplacian polynomial $\\Delta$ is the exponential growth rate of the complexity of finite quotients of $G$. It is bounded below by $m(\\Delta({\\mathbb G}_d))$, where ${\\mathbb G}_d$ is the grid graph of dimension $d$. The growth rates $m(\\Delta({\\mathbb G}_d))$ are asymptotic to $\\log 2d$ as $d$ tends to inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02797","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"}