منابع مشابه
Splitting Multidimensional Necklaces
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...
متن کاملSplitting 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...
متن کاملGenerating Necklaces
A k color n bead necklace is an equivalence class of k ary n tuples under rotation In this paper we analyze an algorithm due to Fredricksen Kessler and Maiorana FKM to show that necklaces can be generated in constant amortized time We also present a new approach to generating necklaces which we conjecture can also be implemented in constant amortized time The FKM algorithm generates a list of n...
متن کاملPerfect Necklaces
We introduce a variant of de Bruijn words that we call perfect necklaces. Fix a finite alphabet. Recall that a word is a finite sequence of symbols in the alphabet and a circular word, or necklace, is the equivalence class of a word under rotations. For positive integers k and n, we call a necklace (k, n)-perfect if each word of length k occurs exactly n times at positions which are different m...
متن کاملSplitting Necklaces and a Generalization of the Borsuk-ulam Antipodal Theorem
We prove a very natural generalization of the Borsuk-Ulam antipodal Theorem and deduce from it, in a very straightforward way, the celebrated result of Alon [1] on splitting necklaces. Alon’s result says that t(k− 1) is an upper bound on the number of cutpoints of an opened t-coloured necklace so that the segments we get can be used to partition the set of vertices of the necklace into k subset...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1987
ISSN: 0001-8708
DOI: 10.1016/0001-8708(87)90055-7