Single-factor coefficient bounds

In a 1993 paper Beauzamy, Trevisan and Wang derived a single-factor coefficient bound, one which limits the max norm (height) of at least one irreducible factor of any univariate integral polynomial A. Their bound is a function of the degree and the weighted norm of A. In the conclusion of their paper they ask whether the max norm of A might already be a single-factor coefficient bound. In 1998 Knuth, citing these authors, asked instead whether there is a constant c such that c times the max norm of A is a single-factor coefficient bound. We present the results of extensive calculations relating to this question. We show that c, if it exists, must be greater than 2 and accrue evidence in support of a conjecture that the answer to Knuth’s question is “no”.