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Zhicheng Gao ; David Laferrière ; Daniel Panario - 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) - 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

  • 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)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: decomposable structures,generating functions,alg-log type,analytic combinatorics,saddle point method,[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]

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