CodeCogs

Calculates the multinomial coefficient with the given arguments.

View versions (1)

Interface

#include <codecogs/maths/combinatorics/arithmetic/multinomial_gamma.h>

using namespace Maths::Combinatorics::Arithmetic;

int multinomial_gamma(int n, int *factors)

This function calculates the multinomial coefficient with the given arguments $k_1, k_2, \ldots k_n$ given by

$(k_1, k_2, \ldots k_n)! = \frac{(k_1 + k_2 + \ldots + k_n)!}{k_1! k_2! \ldots k_n!}$

(1)

Large values of the factors may be given without the fear that computer overflow would occur during intermediate calculations. This is possible with the use of the logarithm of the Gamma function.

References

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

Example 1

#include <codecogs/maths/combinatorics/arithmetic/multinomial_gamma.h>
#include <iostream>
int main()
{
  int factors[4] = {1, 2, 5, 3};
  std::cout << "In the case of the following factors" << std::endl;
  for (int i = 0; i < 4; i++)
    std::cout << factors[i] << "  ";
  std::cout << std::endl << "the multinomial coefficient is" << std::endl;
  std::cout << Maths::Combinatorics::Arithmetic::multinomial_gamma(4, factors) << std::endl;
  return 0;
}

Output:

In the case of the following factors
1  2  5  3
the multinomial coefficient is
27720

Parameters

the number of arguments

factors

the factors of the multinomial, given as an array

Returns

the multinomial coefficient based on the values of the factors

Multinomial_Gamma

Interface

References

Example 1

Parameters

Returns