Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A k-ary necklace is an Ž . equivalence class of k-ary strings under rotation the cyclic group . A k-ary unlabeled necklace is an equivalence class of k-ary strings under rotation and permutation of alphabet symbols. We present new, fast, simple, recursive algoŽ . rit...

This paper develops a constant amortized time algorithm to produce a cyclic cool-lex Gray code for fixed-density binary necklaces, Lyndon words, and pseudo-necklaces. It is the first Gray code for these objects that achieves this time bound. The algorithm is applied: (i) to develop a constant amortized time cyclic Gray code for necklaces, Lyndon words, and pseudo-necklaces ordered by density an...

Some constraint problems have a combinatorial structure where the constraints allow the sequence of variables to be rotated (necklaces), if not also the domain values to be permuted (unlabelled necklaces), without getting an essentially different solution. We bring together the fields of combinatorial enumeration, where efficient algorithms have been designed for (special cases of) some of thes...

Recently, a Gray code for unrestricted binary necklaces and their relatives was discovered by Vajnovszki [Discrete Mathematics & Theoretical Computer Science, to appear]. The Gray code is constructed by modifying the classical FKM algorithm for generating necklaces in lexicographic order. We present a generalisation of Vajnovszki’s algorithm, giving a Gray code for necklaces and their relatives...

A necklace is an equivalence class of binary strings under rotation In this paper we present a Gray code listing of all n bit necklaces with d ones so that i each necklace is listed exactly once by a representative from its equivalence class and ii successive representatives including the last and the rst in the list di er only by the transposition of two bits The total time required is O nN n ...

We argue that due to various restrictions only necklaces and monopolonia survive as potential sources of ultra-high energy cosmic rays, among the topological defects studied so far. Other promising sources which are similar to topological defects are relic superheavy particles. All these sources have an excess of pions (and thus photons) over nucleons at production. We demonstrate that in the c...

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...

This paper develops a constant amortized time algorithm to produce the cyclic cool-lex Gray code for fixed-density binary necklaces, Lyndon words, and pseudo-necklaces. It is the first Gray code for these objects that achieves this time bound. In addition to Gray code order, the algorithms can be easily modified to output the strings in co-lex order.