What Is the Term for Decomposing Numbers into Additive Combinations?

[jopux]

"Factoring" of addition?

Is there a name for "factoring" addition? For example...let's say I'm working in a basis of all integers greater than 3. I can make 7 from 3+4; 8 from 4+4 or 3+5; 9 from 3+3+3 or 4+5 or 6+3...

Is there a name for this? And if so...are there computer programs that will generate these sets for me?

 

[matt grime]

Look up partition functions.

 

[pig]

are there computer programs that will generate these sets for me?

try this

#include <stdio.h>

#define LOWEST 3

int n, c[1024];
FILE *out;

void add (int pos, int a, int sum) {
	int i;
	c[pos]=a;
	if (sum>n) return;
	if (sum==n) {
		for (i=0;i<=pos;i++) fprintf(out, "%d ", c[i]);
		fprintf(out, "\n");
		return;
	}
	for (i=a;i>=LOWEST;i--) add(pos+1, i, sum+i);
}

int main () {
	int i;
	printf("n: ");
	scanf("%d", &n);
	out=fopen("results.txt", "wt");
	for (i=n-LOWEST;i>=LOWEST;i--) add(0, i, i);
	fclose(out);
	return 0;
}

this is very slow, i'll try to think of a way to make it faster.

if source code is not allowed in the math forum, i am sorry, delete the post.