We present a technique to recover f ∈ Q(ζp) where ζp is a primitive pth root of unity for a prime p, given its norm g = f ∗ f̄ in the totally real field Q(ζp + ζ −1 p ). The classical method of solving this problem involves finding generators of principal ideals by enumerating the whole class group associated with Q(ζp), but this approach quickly becomes infeasible as p increases. The apparent h...

Let F [p] denote the set of binary words, with no more 0’s than 1’s, that do not contain the pattern p = (10)1 as a factor for any fixed j ≥ 1. We give the generating function for the integer sequence enumerating, according to the number of 1’s, the words in F [p].