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 d where N n d denotes the number of n bit binary necklaces with d ones This is the rst algorithm for generating necklaces of xed density which is known to achieve this time bound