Determinants of multiplicative Toeplitz matrices
Let . We find explicit conditions on a and b that are necessary and sufficient for f to be a permutation polynomial of . This result allows us to solve a related problem: Let (n ≥ 0, ) be the polynomial defined by the functional equation . We determine all n of the form , α > β ≥ 0, for which is a permutation polynomial of .
This note summarizes a presentation made at the Third International Meeting on Integer Valued Polynomials and Problems in Commutative Algebra. All the work behind it is joint with Scott T. Chapman, and will appear in [2]. Let represent the ring of polynomials with rational coefficients which are integer-valued at integers. We determine criteria for two such polynomials to have the same image set on .