On the theorem of Fredricksen and Maiorana about de Bruijn sequences

Abstract

This work gives an alternative proof for the theorem of Fredricksen and Maiorana [Discrete Math. 23 (1978) 207–210] about constructing a de Bruijn sequence by concatenation of the Lyndon words in lexicographic order. This proof gives the exact position of all the words in the sequence, and allows us to extend this result to the concatenation of any number of the last Lyndon words in increasing order.