combinat::necklaces – necklaces

combinat::necklaces provides functions for counting, generating, and manipulating necklaces.

Further functions are documented theme by theme in separate help pages:

• necklaces with prescribed evaluation: combinat::necklaces::fromEvaluation.

• necklaces with prescribed content: combinat::necklaces::fromContent.

Superdomain

Dom::BaseDomain

Categories

Cat::CombinatorialClass

Axioms

Ax::systemRep

Related Domains:

combinat::lyndonWords

Details:

• A necklace is a word, considered up to a cyclic rotation. For example, [2,1,3,1], [1,3,1,2], [3,1,2,1], and [1,2,1,3] all represent the same necklace.

• If the letters (or beads) of a necklace can be ordered then, by convention, its canonical representative is the lexicographically smallest element in its equivalence class. In the example above, that would be [1,2,1,3].

• A necklace may be periodic, like [1,2,1,2,1,2]. See combinat::lyndonWords for manipulating aperiodic necklaces.

Entries

Changes in MuPAD 3.1

New Function.