We initiate an algebraic approach to study DNA origami structures by associating an element from a monoid to each structure. We identify two types of basic building blocks and describe an DNA origami structure with their composition. These building blocks are taken as generators of a monoid, called origami monoid, and, motivated by the well studied Temperley-Lieb algebras, we identify a set of relations that characterize the origami monoid. We also present several observations about the Green's relations for the origami monoid and study the relations to a cross product of Jones monoids that is a morphic image of an origami monoid.
@article{arxiv.1901.09120,
title = {Algebraic Systems for DNA Origami Motivated from Temperley-Lieb Algebras},
author = {James Garrett and Nataša Jonoska and Hwee Kim and Masahico Saito},
journal= {arXiv preprint arXiv:1901.09120},
year = {2019}
}