ASM Number

Returns the number of alternating sign matrices of the given order.

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Interface
Asm Number
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Interface

C++

Excel

Asm Number

intasm_number( int n )

A direct formula for calculating the number of alternating sign matrices of order n is:

$\prod_{i = 0}^{n - 1} \frac{(3i + 1)!}{(n + i)!}$

(2)

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/sequences/asm_number.h>
#include <iostream>
int main()
{
  for (int i = 0; i < 10; i++)
    std::cout << i << " " << Maths::Combinatorics::Sequences::asm_number(i) << std::endl;
  return 0;
}

Output:

0 1
1 1
2 2
3 7
4 42
5 429
6 7436
7 218348
8 10850216
9 188958604

Parameters

n	the order of the matrices

Returns

the number of alternating matrices of order n

Authors

Lucian Bentea (August 2005)

Source Code

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