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The variance in the winding number of various random fractal curves, including the self-avoiding walk, the loop-erased random walk, contours of Fortuin-Kastelyn clusters, and stochastic Loewner evolution, has been studied by numerous researchers. Usually the focus has been on the winding at the end points. We measure the variance in winding number at(More)
We prove a conjecture of Cohn and Propp, which refines a conjecture of Bosley and Fidkowski about the symmetry of the set of alternating sign matrices (ASMs). We examine data arising from the representation of an ASM as a collection of paths connecting 2n vertices and show it to be invariant under the dihedral group D 2n rearranging those vertices, which is(More)
Different types of robots help to fulfill simple work on their own like simple pick-and-place, handling and mounting tasks over long-lasting periods with no loss of accuracy and speed. However, regarding to products produced in small numbers the programming of those robots can be very time-consuming and workers have to be trained in programming the(More)
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