Splitting Multidimensional Necklaces and Measurable Colorings of Euclidean Spaces
نویسندگان
چکیده
منابع مشابه
Splitting Necklaces and Measurable Colorings of the Real Line
A (continuous) necklace is simply an interval of the real line colored measurably with some number of colors. A well-known application of the Borsuk-Ulam theorem asserts that every k-colored necklace can be fairly split by at most k cuts (from the resulting pieces one can form two collections, each capturing the same measure of every color). Here we prove that for every k ≥ 1 there is a measura...
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The well-known “splitting necklace theorem” of Alon [1] says that each necklace with k · ai beads of color i = 1, . . . , n can be fairly divided between k “thieves” by at most n(k − 1) cuts. Alon deduced this result from the fact that such a division is possible also in the case of a continuous necklace [0, 1] where beads of given color are interpreted as measurable sets Ai ⊂ [0, 1] (or more g...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2015
ISSN: 0895-4801,1095-7146
DOI: 10.1137/130948239