On Lewin and Vitek's conjecture about the exponent set of primitive matrices

Abstract

M. Lewin and Y. Vitek conjecture that every integer ⩽[12wn] + 1 = [12(n2−2n + 2)] + 1 is the exponent of some n×n primitive matrix. In this paper we prove that this conjecture is true except for n = 11. The problem of determining the exponent set En is completely solved.