CodeCogs

Computes the product of two permutations.

Interface

#include <codecogs/maths/combinatorics/permutations/multiplication.h>

using namespace Maths::Combinatorics::Permutations;

std::vector<int> multiplication(int n, int *p1, int *p2)

If $\sigma$ and $\tau$ are permutations, given by

$\sigma = \left( \begin{array}{cccc} 1 & 2 & \ldots & n \cr \sigma(1) & \sigma(2) & \ldots & \sigma(n) \end{array} \right)$

(1)

and

$\tau = \left( \begin{array}{cccc} 1 & 2 & \ldots & n \cr \tau(1) & \tau(2) & \ldots & \tau(n) \end{array} \right)$

(2)

then the product $\sigma \circ \tau$ is calculated using the following formula

$\sigma \circ \tau = \left( \begin{array}{cccc} 1 & 2 & \ldots & n \cr \sigma(\tau(1)) & \sigma(\tau(2)) & \ldots & \sigma(\tau(n)) \end{array} \right)$

(3)

This function returns the result of the multiplication as a C++ vector object.

Returns

the product of the two permutations, stored as a C++ vector object

Example:

#include <codecogs/maths/combinatorics/permutations/multiplication.h>
#include <iostream>
int main()
{
  int sigma[5] = {5, 2, 1, 4, 3}, tau[5] = {3, 2, 5, 4, 1};
  std::vector<int> result = Maths::Combinatorics::Permutations::multiplication(5, sigma, tau);
  std::cout << "The multiplication of Sigma and Tau is: ";
  std::cout << std::endl;
  for (int i = 0; i < 5; i++)
    std::cout << result[i] << " ";
  std::cout << std::endl;
  std::cout << "This proves one is the inverse of the other.";
  std::cout << std::endl;
  return 0;
}

Output:

The multiplication of Sigma and Tau is:
1 2 3 4 5
This proves one is the inverse of the other.

References

SUBSET, a C++ library of combinatorial routines, http://www.csit.fsu.edu/~burkardt/cpp_src/subset/subset.html

Multiplication

Interface

Returns

Example:

Output:

References