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.

Source : oai:HAL:hal-01352850v1

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]

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