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We show that $|\\mathcal{A}_{\\boldsymbol{\\lambda}}|= \\mathcal{T}(\\boldsymbol{\\lambda})\\,q^{n-m}+\\mathcal{O}(q^{n-m-{1}/{2}})$, where $\\mathcal{T}(\\boldsymbol{\\lambda})$ is the proportion of elements of the symmetric group of $n$ elements with cycle pattern $\\boldsymbol{\\lambda}$ and $m$ is the codimension of $\\mathcal{A}$. 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We show that $|\\mathcal{A}_{\\boldsymbol{\\lambda}}|= \\mathcal{T}(\\boldsymbol{\\lambda})\\,q^{n-m}+\\mathcal{O}(q^{n-m-{1}/{2}})$, where $\\mathcal{T}(\\boldsymbol{\\lambda})$ is the proportion of elements of the symmetric group of $n$ elements with cycle pattern $\\boldsymbol{\\lambda}$ and $m$ is the codimension of $\\mathcal{A}$. 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