# The profile of unlabeled trees

Abstract : We consider the number of nodes in the levels of unlabeled rooted random trees and show that the joint distribution of several level sizes (where the level number is scaled by $\sqrt{n}$) weakly converges to the distribution of the local time of a Brownian excursion evaluated at the times corresponding to the level numbers. This extends existing results for simply generated trees and forests to the case of unlabeled rooted trees.
Keywords :
Type de document :
Communication dans un congrès
Conrado Martínez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.167-172, 2005, DMTCS Proceedings
Domaine :

Littérature citée [19 références]

https://hal.inria.fr/hal-01184024
Contributeur : Coordination Episciences Iam <>
Soumis le : mercredi 12 août 2015 - 15:51:16
Dernière modification le : mercredi 10 mai 2017 - 17:39:14
Document(s) archivé(s) le : vendredi 13 novembre 2015 - 11:39:54

### Fichier

Fichiers éditeurs autorisés sur une archive ouverte

### Identifiants

• HAL Id : hal-01184024, version 1

### Citation

Bernhard Gittenberger. The profile of unlabeled trees. Conrado Martínez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.167-172, 2005, DMTCS Proceedings. 〈hal-01184024〉

### Métriques

Consultations de la notice

## 91

Téléchargements de fichiers