منابع مشابه
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...
متن کاملGray-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 ...
متن کاملOn T-codes and necklaces
This paper describes a newly discovered aspect of T-codes, a family of variable length codes first described by Titchener in the 1980s. We show that the constant-length subsets of codewords generated during the Tcode construction process constitute sets of necklaces. Moreover, we show that these sets are complete except for a small subset which we characterize. Bounds on the number of constant-...
متن کاملA 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 ...
متن کاملGray codes for reflection groups
Let G be a finite group generated by reflections. It is shown that the elements of G can be arranged in a cycle (a "Gray. code") such that each element is obtained from the previous one by applying one of the generators. The case G = d[ ' yields a conventional binary Gray code. These generalized Gray codes provide an efficient wa), to run through the elements of any finite reflection group.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00348-9