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Approximating $\\Pi$ by its restriction $\\Pi^n$ to $[n]\\:= \\{1, \\ldots, n\\},$ the suitably rescaled block counting process $n^{-1}\\#\\Pi^n(tn^{a-1})$ has a deterministic limit, $c(t)$, as $n\\to\\infty.$ An explicit formula for $c(t)$ is provided in Theorem 1.\n  The block size spectrum $(\\mathfrak{c}_{1}\\Pi^n(t), \\ldots, \\mathfrak{c}_{n}\\Pi^n(t)),$ where $\\mathfrak{c}_{i}\\Pi^n(t)$ counts the number of blocks of size $i$ in $\\Pi^n(t),$ captures more refined","authors_text":"Helmut H. 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