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 ORCID1; Rexhep Gjergji 1

  • 1 Department of Mathematics, University of Prishtina

A composition π=π1π2πm 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 π. 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 τ, and according to the sum, over all occurrences of τ, of the first integers in their respective occurrences, where τ 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: Subwords, generating functions, Cramer’s method,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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