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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 $W$). 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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 $W$). 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