An application of the Goulden–Jackson cluster theorem
Algebraic Combinatorics, Volume 5 (2022) no. 6, pp. 1279-1286.

Let A be an alphabet and let F be a set of words with letters in A. We show that the sum of all words with letters in A with no consecutive subwords in F, as a formal power series in noncommuting variables, is the reciprocal of a series with all coefficients 0, 1 or -1. We also explain how this result is related to the work of Dotsenko and Khoroshkin on a closely related problem and to a theorem of Curtis Greene on lattices with Möbius function 0, 1, or -1.

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DOI: 10.5802/alco.210
Classification: 05A05,  05A15
Keywords: Goulden–Jackson cluster theorem, forbidden subwords, Möbius function
Gessel, Ira M. 1

1 Department of Mathematics Brandeis University Waltham, MA 02453, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Gessel, Ira M. An application of the Goulden–Jackson cluster theorem. Algebraic Combinatorics, Volume 5 (2022) no. 6, pp. 1279-1286. doi : 10.5802/alco.210. https://alco.centre-mersenne.org/articles/10.5802/alco.210/

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