Necklace (combinatorics)
In combinatorics, a k-ary necklace of length n is an equivalence class of n-character strings over an alphabet of size k, taking all rotations as equivalent. It represents a structure with n circularly connected beads of up to k different colors.
A k-ary bracelet, also referred to as a turnover (or free) necklace, is a necklace such that strings may also be equivalent under reflection. That is, given two strings, if each is the reverse of the other then they belong to the same equivalence class. For this reason, a necklace might also be called a fixed necklace to distinguish it from a turnover necklace.
Technically, one may classify a necklace as an orbit of the action of the cyclic group on n-character strings, and a bracelet as an orbit of the dihedral group's action.
Read more about Necklace (combinatorics): Aperiodic Necklaces, Products of Necklaces, See Also
Famous quotes containing the word necklace:
“I remember meeting you in a dark dream
Of April, you or some girl,
The necklace of wishes alive and breathing around your throat.”
—John Ashbery (b. 1927)