Multinomial Gamma

Calculates the multinomial coefficient with the given arguments.

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Multinomial Gamma
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Interface

C++

Multinomial Gamma

intmultinomial_gamma(	int	`n`
	int*	`factors`	)

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

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

(2)

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

n	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

Authors

Lucian Bentea (August 2005)

Source Code

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