Gray-ordered Binary Necklaces

Gray-ordered Binary Necklaces

A k-ary necklace of order n is an equivalence class of strings of length n of symbols from {0, 1, . . . , k − 1} under cyclic rotation. In this paper we define an ordering on the free semigroup on two generators such that the binary strings of length n are in Gray-code order for each n. We take the binary necklace class representatives to be the least of each class in this ordering. We examine ...

A Gray Code for Necklaces of Fixed Density

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 ...

Gray codes for necklaces and Lyndon words of arbitrary base

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...

Ordered Binary Decision Diagramsin

A Gray code for fixed-density necklaces and Lyndon words in constant amortized time

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...