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Lambda words are sequences obtained by encoding the differences betweenordered elements of the form i+j\theta, where i and j are non-negative integersand 1 < \theta <2. Lambda words are right-infinite words defined over aninfinite 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 athree-letter alphabet. Although the mapping preserves palindromes andnon-palindromes of the Lambda word, the resulting Gamma word is not rich.

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