{"paper":{"title":"Transpositional sequences and multigraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alissa Ellis Yazinski, Donald Silberger, Raymond R. Fletcher","submitted_at":"2019-04-22T01:53:37Z","abstract_excerpt":"When ${\\bf t} := \\langle t_1,t_2,\\ldots,t_k\\rangle$ is a sequence of transpositions on the finite set $n:=\\{0,1,\\ldots,n-1\\}$, then $\\bigcirc{\\bf t}:= t_1\\circ t_2\\circ\\cdots\\circ t_k$ denotes the compositional product of the sequence. Our paper treats the set ${\\rm Prod}({\\bf t})$ of all $\\bigcirc{\\bf s}$, where ${\\bf s}$ is a sequence obtained by rearranging the terms of ${\\bf t}$. The paper characterizes the set of all transpositional sequences ${\\bf t}$ for which ${\\rm Prod}({\\bf t})$ is the subset of a single congugacy class in the symmetric group ${\\rm Sym}(n)$; we call such ${\\bf t}$ {\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09694","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"}