{"paper":{"title":"Vector spaces and Grassmann graphs over residue class rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjian Lv, Kaishun Wang, Li-Ping Huang","submitted_at":"2017-05-12T14:51:49Z","abstract_excerpt":"Let $\\mathbb{Z}_{p^s}$ be the residue class ring of integers modulo $p^s$, where $p$ is a prime number and $s$ is a positive integer. Using matrix representation and the inner rank of a matrix, we study the intersection, join, dimension formula and dual subspaces on vector subspaces of $\\mathbb{Z}^n_{p^s}$. Based on these results, we investigate the Grassmann graph $G_{p^s}(n,m)$ over $\\mathbb{Z}_{p^s}$. $G_{p^s}(n,m)$ is a connected vertex-transitive graph, and we determine its valency, clique number and maximum cliques. Finally, we characterize the automorphisms of $G_{p^s}(n,m)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04610","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"}