{"paper":{"title":"Involution Products in Coxeter Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Peter J. Rowley, Sarah B. Hart","submitted_at":"2014-05-13T07:20:27Z","abstract_excerpt":"For $W$ a Coxeter group, let $\\mathcal{W} = \\{ w \\in W \\;| \\; w = xy \\; \\mbox{where} \\; x, y \\in W \\; \\mbox{and} \\; x^2 = 1 = y^2 \\}$. If $W$ is finite, then it is well known that $W = \\mathcal{W}$. Suppose that $w \\in \\mathcal{W}$. Then the minimum value of $\\ell(x) + \\ell(y) - \\ell(w)$, where $x, y \\in W$ with $w = xy$ and $x^2 = 1 = y^2$, is called the \\textit{excess} of $w$ ($\\ell$ is the length function of $W$). The main result established here is that $w$ is always $W$-conjugate to an element with excess equal to zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3051","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"}