Mansour, Toufik and Sirhan, Basel O. - Counting l-letter subwords in compositions

dmtcs:376 - Discrete Mathematics & Theoretical Computer Science, January 1, 2006, Vol. 8
Counting l-letter subwords in compositions

Authors: Mansour, Toufik and Sirhan, Basel O.

Let ℕ be the set of all positive integers and let A be any ordered subset of ℕ. Recently, Heubach and Mansour enumerated the number of compositions of n with m parts in A that contain the subword τ exactly r times, where τ∈{111,112,221,123}. Our aims are (1) to generalize the above results, i.e., to enumerate the number of compositions of n with m parts in A that contain an ℓ-letter subword, and (2) to analyze the number of compositions of n with m parts that avoid an ℓ-letter pattern, for given ℓ. We use tools such as asymptotic analysis of generating functions leading to Gaussian asymptotic.


Volume: Vol. 8
Published on: January 1, 2006
Submitted on: March 26, 2015
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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