Zhicheng Gao ; David Laferrière ; Daniel Panario
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Asymptotics of Decomposable Combinatorial Structures of Alg-Log Type With Positive Log Exponent
dmtcs:2798 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2010,
DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)
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https://doi.org/10.46298/dmtcs.2798
Asymptotics of Decomposable Combinatorial Structures of Alg-Log Type With Positive Log ExponentConference paper
Authors: Zhicheng Gao 1; David Laferrière 1; Daniel Panario 1
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Zhicheng Gao;David Laferrière;Daniel Panario
1 School of Mathematics and Statistics [Ottawa]
We consider the multiset construction of decomposable structures with component generating function C(z) of alg-log type, 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.
Volume: DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)