Ribbon tiles are polyominoes consisting of n squares laid out in a path, each step of which goes north or east. Tile invariants were rst introduced in P1], where a full basis of invariants of ribbon tiles was conjectured. Here we present a complete proof of the conjecture, which works by associating ribbon tiles with certain polygons in the complex plane, and deriving invariants from the signed...

Recent works in algebraic combinatorics have brought up to date the importance of certain planar structures, called ribbon tableaux, which are generalizations of Young tableaux. This paper gives an algorithm to eeciently distribute, using PVM, the computation of the set of all ribbon tableaux of given shape and weight. It also provides a way to compute the spin polynomials associated to those s...

A graphene nanoribbon with zigzag edges has a gapped magnetic ground state with an antiferromagnetic interedge superexchange interaction. We present a theory based on asymptotic properties of the Dirac-model ribbon wave function which predicts W-2 and W-1 ribbon-width dependencies for the superexchange interaction strength and the charge gap, respectively. We find that, unlike the case of conve...

A repetitive crystal-like pattern is spontaneously formed upon the twisting of straight ribbons. The pattern is akin to a tessellation with isosceles triangles, and it can easily be demonstrated with ribbons cut from an overhead transparency. We give a general description of developable ribbons using a ruled procedure where ribbons are uniquely described by two generating functions. This constr...