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.

Source : oai:HAL:hal-00961119v1

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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