Example of necklace splitting with k = 2 (i.e. two partners), and t = 2 (i.e. two types of beads, here 8 red and 6 green). A 2-split is shown: one partner receives the largest section, and the other receives the remaining two pieces.
Necklace splitting is a picturesque name given to several related problems in combinatorics and measure theory. Its name and solutions are due to mathematicians Noga Alon[1] and Douglas B. West.[2]
The basic setting involves a necklace with beads of different colors. The necklace should be divided between several partners (e.g. thieves), such that each partner receives the same amount of every color. Moreover, the number of cuts should be as small as possible (in order to waste as little as possible of the metal in the links between the beads).
^Alon, Noga; West, Douglas B. (December 1986). "The Borsuk-Ulam theorem and bisection of necklaces". Proceedings of the American Mathematical Society. 98 (4): 623–628. doi:10.1090/s0002-9939-1986-0861764-9.
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