compile = truefalse

True means compile the iterator. The default is true.

The DeBruijn command returns an iterator that generates m-ary Lyndon words, each with $0<\mathrm{length}\le n$, that together form a de Bruijn sequence.

A de Bruijn sequence is a sequence of the characters 0 to $m-1$, of length $m^n$, that, when considered as a cycle, contains each string of length $n$ exactly once.

$\mathrm{with}\left(\mathrm{Iterator}\right)\&colon;$

$P≔\mathrm{DeBruijn}\left(4\&comma;3\right)\&colon;$

$\mathrm{Print}\left(P\&comma;'\mathrm{showrank}'\right)\&colon;$

 1: 0
 2: 0 0 0 1
 3: 0 0 0 2
 4: 0 0 1 1
 5: 0 0 1 2
 6: 0 0 2 1
 7: 0 0 2 2
 8: 0 1
 9: 0 1 0 2
10: 0 1 1 1
11: 0 1 1 2
12: 0 1 2 1
13: 0 1 2 2
14: 0 2
15: 0 2 1 1
16: 0 2 1 2
17: 0 2 2 1
18: 0 2 2 2
19: 1
20: 1 1 1 2
21: 1 1 2 2
22: 1 2
23: 1 2 2 2
24: 2

$\left[\mathrm{seq}\left(\mathrm{seq}\left(p\left[k\right]\&comma;k=1..\mathrm{length}\left(P\right)\right)\&comma;p=P\right)\right]$

$\left[0\&comma;0\&comma;0\&comma;0\&comma;1\&comma;0\&comma;0\&comma;0\&comma;2\&comma;0\&comma;0\&comma;1\&comma;1\&comma;0\&comma;0\&comma;1\&comma;2\&comma;0\&comma;0\&comma;2\&comma;1\&comma;0\&comma;0\&comma;2\&comma;2\&comma;0\&comma;1\&comma;0\&comma;1\&comma;0\&comma;2\&comma;0\&comma;1\&comma;1\&comma;1\&comma;0\&comma;1\&comma;1\&comma;2\&comma;0\&comma;1\&comma;2\&comma;1\&comma;0\&comma;1\&comma;2\&comma;2\&comma;0\&comma;2\&comma;0\&comma;2\&comma;1\&comma;1\&comma;0\&comma;2\&comma;1\&comma;2\&comma;0\&comma;2\&comma;2\&comma;1\&comma;0\&comma;2\&comma;2\&comma;2\&comma;1\&comma;1\&comma;1\&comma;1\&comma;2\&comma;1\&comma;1\&comma;2\&comma;2\&comma;1\&comma;2\&comma;1\&comma;2\&comma;2\&comma;2\&comma;2\right]$

Knuth, Donald Ervin. The Art of Computer Programming, volume 4, fascicle 2; generating all tuples and permutations, sec. 7.2.1.1, generating all n-tuples, pp. 26-27.

ibid, Algorithm F, prime and preprime string generation, p. 27.

The Iterator[DeBruijn] command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.

The Iterator[DeBruijn] command was updated in Maple 2022.

The n and m parameters were updated in Maple 2022.