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The model may be defined in several equivalent ways, describing alternative ways of performing this random shuffle: Most similarly to the way humans shuffle cards, the Gilbert–Shannon–Reeds model describes the probabilities obtained from a certain mathematical model of randomly cutting and then riffling a deck of cards.
Widely used in many programs, e.g. it is used in Excel 2003 and later versions for the Excel function RAND [8] and it was the default generator in the language Python up to version 2.2. [9] Rule 30: 1983 S. Wolfram [10] Based on cellular automata. Inversive congruential generator (ICG) 1986 J. Eichenauer and J. Lehn [11] Blum Blum Shub: 1986
Cards lifted after a riffle shuffle, forming what is called a bridge which puts the cards back into place After a riffle shuffle, the cards cascade. A common shuffling technique is called the riffle, or dovetail shuffle or leafing the cards, in which half of the deck is held in each hand with the thumbs inward, then cards are released by the thumbs so that they fall to the table interleaved.
Finally, the sorting method has a simple parallel implementation, unlike the Fisher–Yates shuffle, which is sequential. A variant of the above method that has seen some use in languages that support sorting with user-specified comparison functions is to shuffle a list by sorting it with a comparison function that returns random values.
A simple algorithm to generate a permutation of n items uniformly at random without retries, known as the Fisher–Yates shuffle, is to start with any permutation (for example, the identity permutation), and then go through the positions 0 through n − 2 (we use a convention where the first element has index 0, and the last element has index n − 1), and for each position i swap the element ...
The shuffle product was introduced by Eilenberg & Mac Lane (1953). The name "shuffle product" refers to the fact that the product can be thought of as a sum over all ways of riffle shuffling two words together: this is the riffle shuffle permutation. The product is commutative and associative. [2]
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Both free and paid versions are available. It can handle Microsoft Excel .xls and .xlsx files, and also produce other file formats such as .et, .txt, .csv, .pdf, and .dbf. It supports multiple tabs, VBA macro and PDF converting. [10] Lotus SmartSuite Lotus 123 – for MS Windows. In its MS-DOS (character cell) version, widely considered to be ...
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