Innovation in Mathematics: Proceedings of the Second International Mathematica Symposium
Permutation theory has many applications in several fields of science and technology and it also has a charm in itself. Mathematica is particularly suitable for writing combinatorial algorithms because it provides many easy-to-use tools for handling lists. Several combinatorial built-in functions which involve permutations and combinations are available as standard add-on Mathematica packages. They are grouped under the name of DiscreteMath and are described by their author Steven Skiena in his book . In this paper we focus on ranking and unranking procedures and we examine and implement alternative algorithms to the RankPermutations and NthPermutations already contained in the above mentioned add-on packages. Moreover we provide some applications of these ranking procedures in different topics such as probability, statistics and elementary calculus.