# Statistics for 3-letter patterns with repetitions in compositions

Abstract : A composition $\pi = \pi_1 \pi_2 \cdots \pi_m$ of a positive integer $n$ is an ordered collection of one or more positive integers whose sum is $n$. The number of summands, namely $m$, is called the number of parts of $\pi$. Using linear algebra, we determine formulas for generating functions that count compositions of $n$ with $m$ parts, according to the number of occurrences of the subword pattern $\tau$, and according to the sum, over all occurrences of $\tau$, of the first integers in their respective occurrences, where $\tau$ is any pattern of length three with exactly 2 distinct letters.
Keywords :
Type de document :
Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2016, Vol. 17 no. 3 (3), pp.147-166

Littérature citée [8 références]

https://hal.inria.fr/hal-01352850
Contributeur : Coordination Episciences Iam <>
Soumis le : mardi 16 août 2016 - 15:07:29
Dernière modification le : jeudi 7 septembre 2017 - 01:03:45
Document(s) archivé(s) le : jeudi 17 novembre 2016 - 10:54:05

### Fichier

2801-9921-1-PB.pdf
Accord explicite pour ce dépôt

### Identifiants

• HAL Id : hal-01352850, version 1

### Citation

Armend Shabani, Rexhep Gjergji. Statistics for 3-letter patterns with repetitions in compositions. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2016, Vol. 17 no. 3 (3), pp.147-166. 〈hal-01352850〉

### Métriques

Consultations de la notice

## 34

Téléchargements de fichiers