{"paper":{"title":"Degree Sequence of Random Permutation Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Bhaswar B. Bhattacharya, Sumit Mukherjee","submitted_at":"2015-03-12T04:27:44Z","abstract_excerpt":"In this paper we study the degree sequence of the permutation graph $G_{\\pi_n}$ associated with a sequence $\\pi_n\\in S_n$ of random permutations. Joint limiting distributions of the degrees are established using results from graph and permutation limit theories. In particular, for the uniform random permutation, the joint distribution of the degrees of the vertices labelled $\\lceil nr_1 \\rceil, \\lceil nr_2 \\rceil, \\ldots, \\lceil nr_s \\rceil$ converges (after scaling by $n$) to independent random variables $D_1, D_2, \\ldots, D_s$, where $D_i\\sim \\text{Unif}(r_i, 1-r_i)$, for $r_i\\in [0,1]$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03582","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"}