We prove that the minimal length of a word Sn having the property that it contains exactly Fm+2 distinct subwords of length m for 1 ≤ m ≤ n is Fn + Fn+2. Here Fn is the nth Fibonacci number defined by F1 = F2 = 1 and Fn = Fn−1 + Fn−2 for n > 2. We also give an algorithm that generates a minimal word Sn for each n ≥ 1. 1991 Mathematics Subject Classification: Primary 68R15; Secondary 05C35. 0 In...

A new word-clustering technique is proposed to efficiently build statistically salient class 2-grams from language corpora. By splitting word neighboring characteristics into word-preceding and following directions, multiple (two-dimensional) word classes are assigned to each word. In each side, word classes are merged into larger clusters independently according to preceding or following word ...

A frame is a square uu, where u is an unbordered word. Let F (n) denote the maximum number of distinct frames in a binary word of length n. We count this number for small values of n and show that F (n) is at most bn/2c + 8 for all n and greater than 7n/30− for any positive and infinitely many n. We also show that Fibonacci words, which are known to contain plenty of distinct squares, have only...

If u and v are words, uv denotes their concatenation. For a positive integer n, u = uuu...u (n times). By ǫ we denote the only word of length 0, the empty word. A is the set of all words over A of length n. A = ∪n≥1A n is a free semigroup (an associative set with a binary operation) over A with the group operation being string concatenation. We define A = A ∪ {ǫ}. Definition 1.2. A word u is a ...

Following up on research suggesting an age-related reduction in the rightward extent of the perceptual span during reading (Rayner, Castelhano, & Yang, 2009), we compared old and young adults in an N + 2-boundary paradigm in which a nonword preview of word N + 2 or word N + 2 itself is replaced by the target word once the eyes cross an invisible boundary located after word N. The intermediate w...

As part of an epidemiologic study of hearing disorders in older adults, word recognition performance (NU-6 word lists in quiet and in competing message) was evaluated for 3189 adults grouped by age (48-59 years, n = 1176; 60-69 years, n = 979; 70-79 years, n = 794; 80-92 years, n = 240). Overall, scores for all measures were worse for older age groups and worse for men than for women. Word reco...

This paper describes a new powerful statistical language model based on N-gram model for Japanese speech recognition. In English, a sentence is written word-by-word. On the other hand, a sentence in Japanese has no word boundary character. Therefore, a Japanese sentence requires word segmentation by morphemic analysis before the construction of word N-gram. We propose an N-gram based language m...