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 length less than or equal to 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.

This iterator object has the common iterator methods.

$\mathrm{with}\left(\mathrm{Iterator}\right)\:$

$P≔\mathrm{DeBruijn}\left(4\,3\right)\:$

$\mathrm{Print}\left(P\,'\mathrm{showrank}'\right)\:$

           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

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

$\left[0\,0\,0\,0\,1\,0\,0\,0\,2\,0\,0\,1\,1\,0\,0\,1\,2\,0\,0\,2\,1\,0\,0\,2\,2\,0\,1\,0\,1\,0\,2\,0\,1\,1\,1\,0\,1\,1\,2\,0\,1\,2\,1\,0\,1\,2\,2\,0\,2\,0\,2\,1\,1\,0\,2\,1\,2\,0\,2\,2\,1\,0\,2\,2\,2\,1\,1\,1\,1\,2\,1\,1\,2\,2\,1\,2\,1\,2\,2\,2\,2\right]$

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.