منابع مشابه
Perfect 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 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 کاملDynamics of Cosmic Necklaces
We perform numerical simulations of cosmic necklaces (systems of monopoles connected to two strings each) and investigate the conditions under which monopoles annihilate. When the total monopole energy is large compared to the string energy, we find that the string motion is no longer periodic, and thus the strings will be chopped up by self intersection. When the total monopole energy is much ...
متن کاملNecklaces , Convolutions , and X +
We give subquadratic algorithms that, given two necklaces each with n beads at arbitrary positions, compute the optimal rotation of the necklaces to best align the beads. Here alignment is measured according to the `p norm of the vector of distances between pairs of beads from opposite necklaces in the best perfect matching. We show surprisingly different results for p = 1, p = 2, and p =∞. For...
متن کاملSplitting 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...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2016
ISSN: 0196-8858
DOI: 10.1016/j.aam.2016.05.002