Sign — Permutations

Calculates the sign of the given permutation.

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Interface

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

using namespace Maths::Combinatorics::Permutations;

int sign(int n, int *p)

A permutation can always be replaced by a sequence of pairwise transpositions. A given permutation can be represented by many different such transposition sequences, but the number of such transpositions will always be odd or always be even. If the number of transpositions is even or odd, the permutation is said to be even or odd. This function returns a corresponding value of $-1$ if the permutation is odd, and a value of $1$ if it is even.

Example:

#include <codecogs/maths/combinatorics/permutations/sign.h>
#include <iostream>
int main()
{
  int alpha[5] = {4, 3, 5, 1, 2};
  std::cout << "The sign of the Alpha permutation is: ";
  std::cout << Maths::Combinatorics::Permutations::sign(5, alpha) << std::endl;
  return 0;
}

Output:

The sign of the Alpha permutation is: -1

References

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

Parameters

the size of the permutation

the actual permutation stored as an array

Returns

the sign of the given permutation