We prove several versions of Alon's necklace-splitting theorem, subject to additional constraints, as illustrated by the following results. (1) The “almost equicardinal theorem” claims that, without increasing number cuts, one guarantees existence a fair splitting such that each thief is allocated almost same pieces necklace (including “degenerate pieces” if they exist), provided thieves $r=p^\...

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...

We highlight a question about binary necklaces, i.e., equivalence classes of binary strings under rotation. Is there a way to choose representatives of the n-bit necklaces so that the subposet of the Boolean lattice induced by those representatives has a symmetric chain decomposition? Alternatively, is the quotient of the Boolean lattice Bn, under the action of the cyclic group Zn, a symmetric ...

We studied the behavioral effects of necklace-style radiotransmitters on breeding male western burrowing owls (Athene cunicularia hypugaea) in 2 areas of northwestern Texas, USA, in 2004 and 2005. We tested the hypothesis that transmittered owls would spend time interacting with their necklaces and as a result spend less time in vigilance and resting activities than would nontransmittered owls....

Cosmic strings have gained a great interest, since they are formed in a large class of brane inflationary models. The most interesting story is that cosmic strings in brane models are distinguished in future cosmological observations. If the strings in brane models are branes or superstrings that can move along compactified space, and also if there are degenerated vacua along the compactified s...

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...

Certain enumeration questions arising from the study of binary necklaces are solved. Applications and interpretations are provided.

We study weakly coupled SU(N) N = 4 super Yang-Mills theory on R × S at infinite N , which has interesting thermodynamics, including a Hagedorn transition, even at zero Yang-Mills coupling. We calculate the exact one-loop partition function below the Hagedorn temperature. Our calculation employs the representation of the one-loop dilatation operator as a spin chain Hamiltonian acting on neighbo...