## Armend Shabani ; Rexhep Gjergji - Statistics for 3-letter patterns with repetitions in compositions

dmtcs:2156 - Discrete Mathematics & Theoretical Computer Science, May 31, 2016, Vol. 17 no. 3 - https://doi.org/10.46298/dmtcs.2156
Statistics for 3-letter patterns with repetitions in compositionsArticle

Authors: Armend Shabani 1; Rexhep Gjergji 1

• 1 Department of Mathematics, University of Prishtina

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.

Volume: Vol. 17 no. 3
Section: Combinatorics
Published on: May 31, 2016
Submitted on: May 5, 2015
Keywords: Cramer’s method,Subwords, generating functions,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]