KLyndonWords

The Lyndon words of length $n$ over a $k$-letter alphabet: aperiodic necklaces, strictly less than every nontrivial rotation.

SageMathLyndonWords(n, k)↗

KLyndonWords(n, k)the Lyndon words of length $n$ over a $k$-letter alphabet: aperiodic necklaces, strictly less than every nontrivial rotation

Typed signatures

Type	Package	Applies
(integer<0..>, integer<0..>) -> indexed_collection<list<integer>>	combinatorics	always

Domain: Collections

Details

• Count is $\frac{1}{n}\sum_{d \mid n} \mu(d) \, k^{n/d}$; specializes to LyndonWords at $k=2$.

Enumeration

Examples

1 more kept as data, checked against the oracles

Basic #

$Count(KLyndonWords(4, 3)) = 18$

live ↗

In$\mathrm{Count}(\mathrm{KLyndonWords}(4, 3))$Out$18$

The first element in enumeration order

live ↗

In$\mathrm{KLyndonWords}(4, 3)[1]$Out$\bigl\lbrack1, 1, 1, 2\bigr\rbrack$

About

Examples	3
Crosswalk	SageMath

See also: LyndonWords, KNecklaces