Abstract
A $k$-ary necklace of order $n$ is an equivalence class of strings of length $n$ of symbols from $\{0,1,\ldots,k-1\}$ 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 the properties of this ordering and in particular prove that all binary strings factor canonically as products of these representatives. We conjecture that stepping from one representative of length $n$ to the next in this ordering requires only one bit flip, except at easily characterized steps.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
