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Was (wer) ist permutation modulation - definition
![[[Waterfall plot]] of a 146.52 MHz radio carrier, with amplitude modulation by a 1,000 Hz sinusoid. Two strong sidebands at + and - 1 kHz from the carrier frequency are shown.](https://commons.wikimedia.org/wiki/Special:FilePath/Waterfall AM.jpg?width=200 "[[Waterfall plot]] of a 146.52 MHz radio carrier, with amplitude modulation by a 1,000 Hz sinusoid. Two strong sidebands at + and - 1 kHz from the carrier frequency are shown.")
![A carrier, frequency modulated by a 1,000 Hz sinusoid. The [[modulation index]] has been adjusted to around 2.4, so the carrier frequency has small amplitude. Several strong sidebands are apparent; in principle an infinite number are produced in FM but the higher-order sidebands are of negligible magnitude.](https://commons.wikimedia.org/wiki/Special:FilePath/Waterfall FM.jpg?width=200 "A carrier, frequency modulated by a 1,000 Hz sinusoid. The [[modulation index]] has been adjusted to around 2.4, so the carrier frequency has small amplitude. Several strong sidebands are apparent; in principle an infinite number are produced in FM but the higher-order sidebands are of negligible magnitude.")
Wikipedia
The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms, especially of sorting algorithms, which operate on random permutations. Suppose, for example, that we are using quickselect (a cousin of quicksort) to select a random element of a random permutation. Quickselect will perform a partial sort on the array, as it partitions the array according to the pivot. Hence a permutation will be less disordered after quickselect has been performed. The amount of disorder that remains may be analysed with generating functions. These generating functions depend in a fundamental way on the generating functions of random permutation statistics. Hence it is of vital importance to compute these generating functions.
The article on random permutations contains an introduction to random permutations.
