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Asymptotics of Decomposable Combinatorial Structures of Alg-Log Type With Positive Log Exponent
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010).

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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. 
@article{DMTCS_2010_special_258_a34,
     author = {Gao, Zhicheng and Laferri\`ere, David and Panario, Daniel},
     title = {Asymptotics of {Decomposable} {Combinatorial} {Structures} of {Alg-Log} {Type} {With} {Positive} {Log} {Exponent}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)},
     year = {2010},
     doi = {10.46298/dmtcs.2798},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2798/}
}
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Gao, Zhicheng; Laferrière, David; Panario, Daniel. Asymptotics of Decomposable Combinatorial Structures of Alg-Log Type With Positive Log Exponent. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010). doi : 10.46298/dmtcs.2798. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2798/

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