Browsing Waterloo Research by Author "Shallit, Jeffrey"
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Critical exponents of infinite balanced words
Rampersad, Narad; Shallit, Jeffrey; Vandomme, Élise (Elsevier, 2019-07-19)Over an alphabet of size 3 we construct an infinite balanced word with critical exponent 2 + root2/2. Over an alphabet of size 4 we construct an infinite balanced word with critical exponent (5 + root5)/4. Over larger ... -
Decidability and k-Regular Sequences
Krenn, Daniel; Shallit, Jeffrey (Elsevier, 2020-05)In this paper we consider a number of natural decision problems involving k-regular sequences. Specifically, they arise from considering • lower and upper bounds on growth rate; in particular boundedness, • images, • ... -
The number of valid factorizations of Fibonacci prefixes
Bonardo, Pierre; Frid, Anna E.; Shallit, Jeffrey (Elsevier, 2019-07-05)We establish several recurrence relations and an explicit formula for V(n), the number of factorizations of the length-n prefix of the Fibonacci word into a (not necessarily strictly) decreasing sequence of standard Fibonacci ... -
The number of valid factorizations of Fibonacci prefixes
Bonardo, Pierre; Frid, Anna E.; Shallit, Jeffrey (Elsevier, 2019-07-05)We establish several recurrence relations and an explicit formula for , the number of factorizations of the length-n prefix of the Fibonacci word into a (not necessarily strictly) decreasing sequence of standard Fibonacci ... -
Subword complexity and power avoidance
Shallit, Jeffrey; Shur, Arseny (Elsevier, 2019-11-05)We begin a systematic study of the relations between subword complexity of infinite words and their power avoidance. Among other things, we show that –the Thue–Morse word has the minimum possible subword complexity over ...