Li Dong ; Zhicheng Gao ; Daniel Panario - The Size of the rth Smallest Component in Decomposable Structures with a Restricted Pattern

dmtcs:3526 - Discrete Mathematics & Theoretical Computer Science, January 1, 2007, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) - https://doi.org/10.46298/dmtcs.3526
The Size of the rth Smallest Component in Decomposable Structures with a Restricted PatternArticle

Authors: Li Dong ; Zhicheng Gao 1,2; Daniel Panario 1

  • 1 School of Mathematics and Statistics [Ottawa]
  • 2 Center for Combinatorics [Nankai]

In our previous work [paper1], we derived an asymptotic expression for the probability that a random decomposable combinatorial structure of size n in the \exp -\log class has a given restricted pattern. In this paper, under similar conditions, we provide the probability that a random decomposable combinatorial structure has a given restricted pattern and the size of its rth smallest component is bigger than k, for r,k given integers. Our studies apply to labeled and unlabeled structures. We also give several concrete examples.


Volume: DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07)
Section: Proceedings
Published on: January 1, 2007
Imported on: May 10, 2017
Keywords: decomposable combinatorial structures,restricted pattern,exp-log class,singularity analysis,rth smallest component.,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]

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