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# Asymptotics of Decomposable Combinatorial Structures of Alg-Log Type With Positive Log Exponent

Abstract : We consider the multiset construction of decomposable structures with component generating function $C(z)$ of alg-log type, $\textit{i.e.}$, $C(z) = (1-z)^{-\alpha} (\log \frac{1}{ 1-z})^{\beta}$. We provide asymptotic results for the number of labeled objects of size $n$ in the case when $\alpha$ is positive and $\beta$ is positive and in the case $\alpha = 0$ and $\beta \geq 2$. The case $0<-\alpha <1$ and any $\beta$ and the case $\alpha > 0$ and $\beta = 0$ have been treated in previous papers. Our results extend previous work of Wright.
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https://hal.inria.fr/hal-01185597
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### Citation

Zhicheng Gao, David Laferrière, Daniel Panario. Asymptotics of Decomposable Combinatorial Structures of Alg-Log Type With Positive Log Exponent. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. pp.289-302, ⟨10.46298/dmtcs.2798⟩. ⟨hal-01185597⟩

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