An Algorithm for Generating a Family of Alternating Knots
An alternating link diagram composed of a set of rectilinear polygons with vertices on the 2-dimensional integer lattice. The polygons are bounded by an axis-aligned square, , which has side length and has the origin at lower left corner. They are also inscribed in a rectangle, , which has its sides parallel to the diagonals of , is symmetric with respect to the central point of , and has sides through the points and . The vertices of the polygons are the lattice nodes lying on the sides of and they are numbered from 0 to .
Article of the Year Award: Outstanding research contributions of 2020, as selected by our Chief Editors. Read the winning articles.