The Size of the rth Smallest Component in Decomposable Structures with a Restricted Pattern

Lihua Dong (1) , Zhicheng Gao (1, 2) , Daniel Panario (1)

1 School of Mathematics and Statistics [Ottawa]
2 CFC - 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.

Mots clés: decomposable combinatorial structures; restricted pattern; exp-log class; singularity analysis; rth smallest component.

Domaines: Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]; Combinatoire [math.CO]; Géométrie algorithmique [cs.CG]

Lihua Dong, Zhicheng Gao, Daniel Panario. The Size of the rth Smallest Component in Decomposable Structures with a Restricted Pattern. 2007 Conference on Analysis of Algorithms, AofA 07, 2007, Juan les Pins, France. pp.403-422, ⟨10.46298/dmtcs.3526⟩. ⟨hal-01184774⟩