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2021•Discrete Mathematics Algorithms and ApplicationsRequires access

Generation of the symmetric group Sn2

Carlos Zequeira Sánchez, Evaristo José Madarro Capó, Guillermo Sosa-Gómez

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Abstract

In various scenarios today, the generation of random permutations has become an indispensable tool. Since random permutation of dimension [Formula: see text] is a random element of the symmetric group [Formula: see text], it is necessary to have algorithms capable of generating any permutation. This work demonstrates that it is possible to generate the symmetric group [Formula: see text] by shifting the components of a particular matrix representation of each permutation.

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What this paper is about

In various scenarios today, the generation of random permutations has become an indispensable tool. Since random permutation of dimension [Formula: see text] is a random element of the symmetric group [Formula: see text], it is necessary to have algorithms capable of generating any permutation. This work demonstrates that it is possible to generate the symmetric group [Formula: see text] by shifting the components of a particular matrix representation of each permutation.

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Available abstract

In various scenarios today, the generation of random permutations has become an indispensable tool. Since random permutation of dimension [Formula: see text] is a random element of the symmetric group [Formula: see text], it is necessary to have algorithms capable of generating any permutation. This work demonstrates that it is possible to generate the symmetric group [Formula: see text] by shifting the components of a particular matrix representation of each permutation.

Key concepts: Symmetric group, Permutation group, Random permutation, Cyclic permutation, Permutation (music), Generalized permutation matrix, Combinatorics, Permutation matrix

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