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Discrete Complex Analysis

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Figure 1.5: The four values f (x), f (y1), f(y 2 ), f(y 3 ) determine uniquely f (x 1 ), f(x 2 ), f (x 3 ) when f is discrete holomorphic, but f (y) is over-determined unless the weights come from parallelograms.
Figure 1.7: The cross-ratio of the centers and intersection points of two circles is given by their intersection angle.
Figure 1.9: A 1-1-correspondence between edge signed planar graphs and regular projections of links helps to manipulate and beautifully draw knots.
Figure 1.11: 2 n walkers on a line in Z 2 recover the binomials n p  . 1 4 12 14 (a) 4-4 18 34 18 (b) 8-8 18 58 14 (c) 8-4 14 58 18 (d) 4-8
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