{"paper":{"title":"Cycle bases of reduced powers of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gregory D. Smith, Richard H. Hammack","submitted_at":"2016-01-12T15:08:52Z","abstract_excerpt":"We define what appears to be a new construction. Given a graph $G$ and a positive integer $k$, the reduced $k$th power of $G$, denoted $G^{(k)}$, is the configuration space in which $k$ indistinguishable tokens are placed on the vertices of $G$, so that any vertex can hold up to $k$ tokens. Two configurations are adjacent if one can be transformed to the other by moving a single token along an edge to an adjacent vertex.\n  The reduced power $G^{(k)}$ is the transition graph of the master Markov chain for $k$ identical and indistinguishable stochastic automata with transition graph $G$. We pres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02896","kind":"arxiv","version":2},"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"}