Locally Restricted Compositions IV. Nearly Free Large Parts and Gap-Freeness

Edward Bender 1 Rodney Canfield 2 Zhicheng Gao 3
1 San Francisco State University - Department of Mathematics
2 Department of Computer Science [Athens GA]
3 School of Mathematics and Statistics [Ottawa]
Abstract : We define the notion of $t$-free for locally restricted compositions, which means roughly that if such a composition contains a part $c_i$ and nearby parts are at least $t$ smaller, then $c_i$ can be replaced by any larger part. Two well-known examples are Carlitz and alternating compositions. We show that large parts have asymptotically geometric distributions. This leads to asymptotically independent Poisson variables for numbers of various large parts. Based on this we obtain asymptotic formulas for the probability of being gap free and for the expected values of the largest part and number distinct parts, all accurate to $o(1)$.
Keywords : restricted compositions largest part distinct parts gaps
Type de document :
Communication dans un congrès
Broutin, Nicolas and Devroye, Luc. 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'12), 2012, Montreal, Canada. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), pp.233-242, 2012, DMTCS Proceedings
Liste complète des métadonnées

Littérature citée [16 références]  Voir  Masquer  Télécharger
https://hal.inria.fr/hal-01197233
Contributeur : Coordination Episciences Iam <>
Soumis le : vendredi 11 septembre 2015 - 12:54:54
Dernière modification le : mardi 7 mars 2017 - 15:19:04
Document(s) archivé(s) le : mardi 29 décembre 2015 - 00:34:16

Fichier

dmAQ0119.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-01197233, version 1

Collections

INSMI | TDS-MACS

Citation

Edward Bender, Rodney Canfield, Zhicheng Gao. Locally Restricted Compositions IV. Nearly Free Large Parts and Gap-Freeness. Broutin, Nicolas and Devroye, Luc. 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'12), 2012, Montreal, Canada. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), pp.233-242, 2012, DMTCS Proceedings. 〈hal-01197233〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

219

Téléchargements de fichiers

141

Contact


archive-ouverte@inria.fr