compile = truefalse

True means compile the iterator. The default is true.

rank = nonnegint

Specify the starting rank of the iterator. The default is one. Passing a value greater than one causes the iterator to skip the lower ranks; this can be useful when parallelizing iterators. The starting rank reverts to one when the iterator is reset, reused, or copied.

The Necklace command returns an iterator that generates all m-ary necklaces of length n, in lexicographic order. The alphabet consists of the integers from 0 to $m-1$; if $m\=0$ the alphabet is empty.

The n parameter is the length of the necklace.

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

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

$P≔\mathrm{Necklace}\left(4\,2\right)\:$

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

1: 0 0 0 0
2: 0 0 0 1
3: 0 0 1 1
4: 0 1 0 1
5: 0 1 1 1
6: 1 1 1 1

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

$6$

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

$4$

$\mathrm{Unrank}\left(P\,3\right)$

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

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[Necklace] command was introduced in Maple 2020.

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

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

The n and m parameters were updated in Maple 2022.