Dejeanʹs conjecture and letter frequency

We prove two cases of a strong version of Dejeanʹs conjecture involving extremal letter frequencies. The results are that there exist an infinite ( 5 4 + ) -free word over a 5 letter alphabet with letter frequency 1 6 and an infinite ( 6 5 + ) -free word over a 6 letter alphabet with letter frequency 1 5 .