# Generating function

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Analysis of Algorithms Princeton University. This course teaches a calculus that enables precise quantitative predictions of large combinatorial structures. In addition, this course covers generating functions and real asymptotics and then introduces the symbolic method in the context of applications in the analysis of algorithms and basic structures such as permutations, trees, strings, words, and mappings. Analysis of Algorithms aims to enable precise quantitative predictions of the ...

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Fig 1: Evidence of scarring: Superposition of the first 3300 iterations of a wave function initiated by two different generating functions (a and c in fig 4) with wavelength chosen to be a fraction of the associated classical repelling orbit. Upper two figures show superposition of phase amplitudes and lower two the corresponding superimposed probability distributions of the squared amplitudes, showing evident scarring.