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 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.