CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search De Bruijn sequence for k = 2 and n = 2 In combinatorial mathematics , a k -ary De Bruijn sequence B ( k , n ) of order n , named after the Dutch mathematician Nicolaas Govert de Bruijn , is a cyclic sequence of a given alphabet A with size k for which every possible subsequence of length n in A appears as a sequence of consecutive characters exactly once. Each B ( k , n ) has length k n . There are distinct De Bruijn sequences B ( k , n ) . According to de Bruijn, [ 1 ] the existence of De Bruijn sequences for each order together with the above properties were first proved, for the case of alphabets with two elements, by Camille Flye Sainte-Marie in 1894, [ 2 ] whereas the generalization to larger alphabets is originally due to Tanja van Aardenne-Ehrenfest and himself. 1 H...