=count n (r, 0)count n (r -1, 0). Hence there are count n (r, 0)count n (r -1, 0) standard bars of length r . To create a mathematical torsion bar there is a further requirement that none of the building block bars is semi-infinite (i.e. has length 0 = ∞). So the number of mathematical torsion bars of length r is the number of ways to combine n bars of length at least r but less than 0 = ∞, minus the number of ways to combine n bars of length strictly greater than r but less than 0 = ∞. Hence the number of mathematical torsion bars of length r in the product barcode is