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- Necklace_splitting_problem abstract "In mathematics, and in particular combinatorics, the necklace splitting problem arises in a variety of contexts including exact division; its picturesque name is due to mathematicians Noga Alon and Douglas B. West.Suppose a necklace, open at the clasp, has k ·n beads. There are k · ai beads of colour i, where 1 ≤ i ≤ t. Then the necklace splitting problem is to find a partition of the necklace into k parts (not necessarily contiguous), each of which has exactly ai beads of colour i; such a split is called a k-split. The size of the split is the number of cuts that are needed to separate the parts (the opening at the clasp is not included). Inevitably, one interesting question is to find a split of minimal size.Alon explains that the problem of finding k-splittings of small size arises naturally when k mathematically oriented thieves steal a necklace with k · ai jewels of type i, and wish to divide it fairly between them, wasting as little as possible of the metal in the links between the jewels.If the beads of each colour are contiguous on the open necklace, then any k splitting must contain at least k − 1 cuts, so the size is at least (k − 1)t. Alon and West use the Borsuk-Ulam theorem to prove that a k-splitting can always be achieved with this number of cuts. Alon uses these and related ideas to state and prove a generalization of the Hobby–Rice theorem.".
- Necklace_splitting_problem thumbnail Necklace_cropped.png?width=300.
- Necklace_splitting_problem wikiPageID "20417521".
- Necklace_splitting_problem wikiPageRevisionID "594751610".
- Necklace_splitting_problem hasPhotoCollection Necklace_splitting_problem.
- Necklace_splitting_problem subject Category:Combinatorics_on_words.
- Necklace_splitting_problem subject Category:Discrete_geometry.
- Necklace_splitting_problem subject Category:Fair_division.
- Necklace_splitting_problem subject Category:Mathematical_problems.
- Necklace_splitting_problem comment "In mathematics, and in particular combinatorics, the necklace splitting problem arises in a variety of contexts including exact division; its picturesque name is due to mathematicians Noga Alon and Douglas B. West.Suppose a necklace, open at the clasp, has k ·n beads. There are k · ai beads of colour i, where 1 ≤ i ≤ t.".
- Necklace_splitting_problem label "Necklace splitting problem".
- Necklace_splitting_problem sameAs m.04zyptb.
- Necklace_splitting_problem sameAs Q6985587.
- Necklace_splitting_problem sameAs Q6985587.
- Necklace_splitting_problem wasDerivedFrom Necklace_splitting_problem?oldid=594751610.
- Necklace_splitting_problem depiction Necklace_cropped.png.
- Necklace_splitting_problem isPrimaryTopicOf Necklace_splitting_problem.
