  A classical result of Fekete gives necessary conditions on a compact set in
the complex plane so that it contains infinitely many sets of conjugate
algebraic integers. We prove an effective version of Fekete's theorem in terms
of a height function. As an application, we give a lower bound on the growth of
the leading coefficient of certain polynomial sequences, generalizing a result
by Schur. Lastly, we give an upper bound on minimal asymptotics of height over
sequences of algebraic numbers.
