Journal of Integer Sequences, Vol. 16 (2013), Article 13.3.4

Lambda Words: A Class of Rich Words Defined Over an Infinite Alphabet

Norman Carey
CUNY Graduate Center
365 Fifth Avenue
New York, NY 10016


Lambda words are sequences obtained by encoding the differences between ordered elements of the form i + jθ, where i and j are non-negative integers and 1 < θ < 2. Lambda words are right-infinite words defined over an infinite alphabet that have connections with Sturmian words, Christoffel words, and interspersion arrays. We show that Lambda words are infinite rich words. Furthermore, any Lambda word may be mapped onto a right-infinite word over a three-letter alphabet. Although the mapping preserves palindromes and non-palindromes of the Lambda word, the resulting Gamma word is not rich.

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(Concerned with sequences A022330 A022331 A167267 A216448 A216763 A216764.)

Received September 15 2012; revised version received January 18 2013; February 17 2013. Published in Journal of Integer Sequences, March 2 2013.

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