Young Number

Calculates the Young tableau number of the given order.

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Interface
Young Number
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Interface

C++

Excel

Young Number

intyoung_number( int n )

This function computes the Young tableau number of order n, using the following recurrent sequence:

$Y(n) = Y(n-1) + (n-1)Y(n-2)$

(2)

with initial values

$Y(1) = 1 \qquad Y(2) = 2$

(3)

Example:

#include <codecogs/maths/combinatorics/sequences/young_number.h>
#include <iostream>
int main()
{
  std::cout << "Young tableau numbers for 0 < n < 10" << std::endl;
  for (int i = 1; i < 10; i++)
    std::cout << i << "  " << Maths::Combinatorics::Sequences::young_number(i) << std::endl;
  return 0;
}

Output:

Young tableau numbers for 0 < n < 10
1  1
2  2
3  4
4  10
5  26
6  76
7  232
8  764
9  2620

References:

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

Parameters

n	the desired order

Returns

the Young tableau number of order n

Authors

Lucian Bentea (August 2005)

Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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