compile = truefalse

True means compile the iterator. The default is true.

rank = nonnegint

Specify the starting rank of the iterator. The default is one. The starting rank reverts to one when the iterator is reset, reused, or copied.

The LyndonWord command returns an iterator that generates all m-ary Lyndon words of length n, in lexicographic order. The alphabet consists of the integers from 0 to $m-1$.

A Lyndon word is an aperiodic necklace. A necklace is an equivalence class of strings under rotation. The representative of a class is the smallest string, lexicographically, in the class.

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

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

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

 1: 0 0 0 1
 2: 0 0 0 2
 3: 0 0 1 1
 4: 0 0 1 2
 5: 0 0 2 1
 6: 0 0 2 2
 7: 0 1 0 2
 8: 0 1 1 1
 9: 0 1 1 2
10: 0 1 2 1
11: 0 1 2 2
12: 0 2 1 1
13: 0 2 1 2
14: 0 2 2 1
15: 0 2 2 2
16: 1 1 1 2
17: 1 1 2 2
18: 1 2 2 2

$\mathrm{Number}\left(P\right)$

$18$

$\mathrm{Rank}\left(P\,\left[0\,1\,1\,2\right]\right)$

$9$

$\mathrm{Unrank}\left(P\,5\right)$

$\left[\begin{array}{cccc}0& 0& 2& 1\end{array}\right]$

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.

Practical Algorithms to Rank Necklaces, Lyndon Words, and de Bruijn Sequences, Joe Sawada and Aaron Williams, Journal of Discrete Algorithms, vol. 43, March 2017, pp. 95-110.

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

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