Conférencier : Narad Rampersad, University of Winnipeg
Abstract: Over a binary alphabet it is well-known that the aperiodic balanced words are exactly the Sturmian words. The repetitions in Sturmian words are well-understood. In particular, there is a formula for the critical exponent (supremum of exponents e such that xe is a factor for some word x) of a Sturmian word. It is known that the Fibonacci word has the least critical exponent over all Sturmian words and this value is (5+√5)/2. However, little is known about the critical exponents of balanced words over larger alphabets. We show that the least critical exponent among ternary balanced words is 2+√2/2 and we construct a balanced word over a four-letter alphabet with critical exponent (5+√5)/4. This is joint work with J. Shallit and E. Vandomme.