Gray-ordered Binary Necklaces

A $k$-ary necklace of order $n$ is an equivalence class of strings of length $n$ of symbols from $\{0,1,\ldots,k-1\}$ 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 ... View More