A chord diagram is formed by choosing some 2n points on a circle (say, at the vertices of a regular polygon) and then connecting them in pairs. It can be represented as a double permutation: a sequence of the 2n values 0,0,1,1,2,2,..., where each value appears twice, and where renumbering the values but keeping the same pairing forms a sequence that is considered to be equivalent. Simply place the values in clockwise order at the chosen points of the circle, and connect pairs of points with equal labels. For instance, the double permutation 0,0,1,2,3,1,3,2, placed clockwise starting at the top vertex of a regular octagon, produces the chord diagram