Dipole Codes Attractively Encode Glue Functions

Abstract

Dipole words are sequences of magnetic dipoles, in which alike elements repel and opposite elements attract. Magnetic dipoles contrast with more general sets of bonding types, called glues, in which pairwise bonding strength is specified by a glue function. We prove that every glue function $g$ has a set of dipole words, called a dipole code, that attractively encodes $g$: the pairwise attractions (positive or non-positive bond strength) between the words are identical to those of $g$. Moreover, we give such word sets of asymptotically optimal length. Similar results are obtained for a commonly used subclass of glue functions.