{"paper":{"title":"On the automorphism group of a Johnson graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ashwin Ganesan","submitted_at":"2014-12-09T14:39:25Z","abstract_excerpt":"The Johnson graph $J(n,i)$ is defined to the graph whose vertex set is the set of all $i$-element subsets of $\\{1,\\ldots,n\\}$, and two vertices are joined whenever the cardinality of their intersection is equal to $i-1$. In Ramras and Donovan [\\emph{SIAM J. Discrete Math}, 25(1): 267-270, 2011], it is conjectured that if $n=2i$, then the automorphism group of the Johnson graph $J(n,i)$ is $S_n \\times \\langle T \\rangle$, where $T$ is the complementation map $A \\mapsto \\{1,\\ldots,n\\} \\setminus A$. We resolve this conjecture in the affirmative. The proof uses only elementary group theory and is b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5055","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"}