Algorithms, software, source code calculate lexicographic order of combinations; compiled program and source code are included. The source code uses two algorithms to find the index or rank for a combination; or find combination for given rank. Both lexicographical algorithms are very fast; the calculations are almost instantaneous. The algorithms can be expanded to cover even more complex sets, such as Powerball/Euromillions types of lottery games. Writing software to automatically calculate the lexicographical order or rank for a combination - and vice versa - is extremely attractive to a large number of computer programmers and scientists. This is the first successful attempt to write software that does the precise calculations for both situations. This computer programmer expanded his knowledge from the combination sets to all four numerical sets: Exponents, permutations, arrangements (and combinations, of course). Included is also a fast and accurate function to calculate combinations of N numbers taken M at a time (such as combinations for a 6-49 lotto game).
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