Abstract:We show a connection between a recent conjecture of Shallit and an older conjecture of Rauzy for infinite words on a finite alphabet. More precisely we show that a Rauzy-like conjecture is equivalent to Shallit's. In passing we correct a misprint in Rauzy's conjecture.
Keywords: combinatorics on words, recurrence function, Sturmian sequences
AMS Subject Classification: 11B05, 68R15