Avoiding substrings in compositons

Mathematics – Combinatorics

Scientific paper

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7 pages; 2 figures (created with the package pstricks); added reference; made slight modifications that relate to new referenc

Scientific paper

A classical result by Guibas and Odlyzko obtained in 1981 gives the generating function for the number of strings that avoid a given set of substrings with the property that no substring is contained in any of the others. In this paper, we give an analogue of this result for the enumeration of compositions that avoid a given set of prohibited substrings, subject to the compositions' length (number of parts) and weight. We also give examples of families of strings to be avoided that allow for an explicit formula for the generating function. Our results extend recent results by Myers on avoidance of strings in compositions subject to weight, but not length.

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