International Scholarly Research Notices / 2012 / Article / Fig 2

Research Article

An Algorithm for Generating a Family of Alternating Knots

Figure 2

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, 𝑆 π‘Ž , which has side length π‘Ž and has the origin at lower left corner. They are also inscribed in a rectangle, 𝑅 π‘Ž , 𝑏 , which has its sides parallel to the diagonals of 𝑆 π‘Ž , is symmetric with respect to the central point of 𝑆 π‘Ž , and has sides through the points ( 0 , π‘Ž βˆ’ 𝑏 ) and ( 0 , π‘Ž βˆ’ 𝑏 + 1 ) . The vertices of the polygons are the lattice nodes lying on the sides of 𝑅 π‘Ž , 𝑏 and they are numbered from 0 to 2 π‘Ž + 1 .

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