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Lexicographic Order Algorithms
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Version
1.0
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.
The first algorithm was discovered by B. P. Buckles
and M. Lybanon (1977). The second algorithm was
created by Ion Saliu (2001). The source code is in the
Power Basic Console Compiler programming language.
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
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