A bijective map r : X −→ X, where X = {x1, · · · , xn} is a finite set, is called a set-theoretic solution of the Yang-Baxter equation (YBE) if the braid relation r12r23r12 = r23r12r23 holds in X. A non-degenerate involutive solution (X, r) satisfying r(xx) = xx, for all x ∈ X, is called squarefree solution. There exist close relations between the square-free set-theoretic solutions of YBE, the...

Department of Engineering, University of Cambridge Trumpington Street, Cambridge CB2 1PZ, U.K. Abstract The optimal shape of cover plates for circular, symmetric retractable roof structures based on a grid of multi-angulated rods connected by revolute joints is considered. It is assumed that these cover plates are co-planar, and hence they are not allowed to overlap in any configuration; they a...