Ranking And Unranking Permutations With Applications
Free (open access)
F. Critani, M. Dall'Aglio & G. Di Biase
Ranking and Unranking Permutations with Applications F. Critani, M. Dall'Aglio, G. Di Biase Dept. of Science, G. D'Annunzio University, viale Pindaro 42, 65127 Pescara, Italy. critani@ sci. unich. it, maglio@sci. unich. it, dibiase @sci. unich. it 1 Introduction 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.