Pseudo-random arrays and codes and designs balanced for residuals in two dimensions
I. M. Chakravarti · 1988
A circular arrangement of the sn letters using the s distinct letters of an alphabet S. such that every n-tuple occurs exactly once as a set of n consecutive symbols of the cycle. is usually called a deBruijn sequence. Aardenne-Ehrenfest and deBruijn (1951) showed that the number of Eulerian circuits in a certain directed graph (called T-graphs by the authors) was the same as the number of such circular arrangements pes) = n n-1 s-n ( s. ')S deBruijn (1975) mentions that the counting problem for s=2 was solved by C. Flye Sainte-Marie in 1894 and gives references to numerous other contributions to the problems of construction and existence of such sequences. An example with s=3 and n=2 is the cycle 11 22 33 13 2. There are 24 such cycles. A subset of these sequences can be generated by dividing 1