{"paper":{"title":"On structures induced by the power sequences of $($\\mathbb{Z}/ m\\mathbb{Z}$, \\cdot)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kelly Isham, Laura Monroe","submitted_at":"2020-02-25T15:44:52Z","abstract_excerpt":"In this paper, we explore the structure of $\\mathbb{Z}/ m\\mathbb{Z}$ in terms of its orbits under modular exponentiation, illustrating this with a sequential power graph that is naturally derived from the orbits by connecting elements of $\\mathbb{Z}/ m\\mathbb{Z}$ in the orbit order in which they appear.\n  We find that this graph has a great deal of fascinating algebraic structure. The connected components are composed of orbits that all share at least one element. The vertex sets of the connected components are shown to depend on the factorization of $m$; in fact, the connected components are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.10980","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.10980/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}