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  1. Home > Articles & Issues >
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  3. Counting l-letter su ...
Article

Counting l-letter subwords in compositions

Toufik Mansour ORCID (1), Basel O. Sirhan (1)
(1) Department of Mathematics [Haïfa]
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Imported on
March 26, 2015
Published on
January 1, 2006
Last modified on
March 31, 2025
Volume 8
vol. 8
DOI
10.46298/dmtcs.376
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https://about.hal.science/hal-authorisation-v1
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Counting l-letter subwords in compositions

Toufik Mansour ORCID (1), Basel O. Sirhan (1)
(1) Department of Mathematics [Haïfa]
Abstract
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.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
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