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Common uses of ball chain are for pull cords on light fixtures [1] and ceiling fans, keychains, and as retaining chains for things such as counter pens, and dogtag chains. Typical width is size 3, or 2.4 mm, steel ball chain. In the jewelry industry, pure 925 sterling silver may be in 1 mm, 1.2 mm, 1.5 mm, 1.8 mm, and 2.2 mm ball chain.
A keychain (/ ˈ k i t ʃ eɪ n / ⓘ) (also keyring) is a small ring or chain of metal to which several keys, or fobs can be attached. The terms keyring & keychain are often used interchangeably to mean both the individual ring, or a combined unit of a ring and fob.
For a given set of n beads, all distinct, the number of distinct necklaces made from these beads, counting rotated necklaces as the same, is n! / n = (n − 1)!. This is because the beads can be linearly ordered in n ! ways, and the n circular shifts of such an ordering all give the same necklace.
Unlike the usual problem of graph coloring, the necklaces are assumed to be aperiodic (not consisting of repeated subsequences), and counted up to rotation (rotating the beads around the necklace counts as the same necklace), but without flipping over (reversing the order of the beads counts as a different necklace). This counting function also ...
The information specifies how many copies the necklace contains of each possible arrangement of black beads. For instance, for k = 2 {\displaystyle k=2} , the specified information gives the number of pairs of black beads that are separated by i {\displaystyle i} positions, for i = 0 , … , ⌊ n / 2 − 1 ⌋ {\displaystyle i=0,\dots ,\lfloor ...
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