10.46298/dmtcs.2156
Shabani, Armend
Armend
Shabani
Gjergji, Rexhep
Rexhep
Gjergji
Statistics for 3-letter patterns with repetitions in compositions
episciences.org
2016
Cramerâ€™s method
Subwords
generating functions
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
contact@episciences.org
episciences.org
2015-05-05T00:00:00+02:00
2021-08-23T23:09:16+02:00
2016-05-31
en
Journal article
https://dmtcs.episciences.org/2156
https://hal.archives-ouvertes.fr/hal-01352850v1
1365-8050
PDF
1
Discrete Mathematics & Theoretical Computer Science ; Vol. 17 no. 3 ; Combinatorics ; 1365-8050
International audience
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.