The major challenge when working with permutations is that the factorial function gets very, very large very, very quickly. The BigInteger data type was introduced in the .NET Framework 4.0; it ...

This note discusses sufficient conditions for a function of permutations (j1,⋯,jn) of the integers 1,2,⋯,n to have a minimum at the permutation (j1 *,⋯,jn *) and derives a solution algorithm that is ...

This is a list of permutation puzzles that can be used as examples. Note that the first three puzzles only work well on computer screens, while the latter three exist as physical objects. Cruzzle I ...

This repository contains the implementation of Birkhoff Extension (BE), a novel method for solving combinatorial optimization problems over permutations. BE provides a continuous, almost-everywhere ...

This is a preview. Log in through your library . Abstract The paper contains a simple, direct derivation of the generating functions for a class of permutations generalizing the up-down permutations.