Compositions Calculator

A simple tool to find and visualize the resulting unique sums you get when you sum compositions of a set of numbers.

Compositions - Combinations with replacement

Example

Number Set - {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

The number of ways you can arrange compositions of this set when you pick 5 (with replacement) is 3003 and those compositions have 51 unique summations.

0: 1
1: 1
2: 2
3: 3
4: 5
5: 7
6: 10
7: 13
8: 18
9: 23
10: 30
11: 36
12: 45
13: 53
14: 63
15: 72
16: 83
17: 92
18: 103
19: 111
20: 121
21: 127
22: 134
23: 137
24: 141
25: 141
26: 141
27: 137
28: 134
29: 127
30: 121
31: 111
32: 103
33: 92
34: 83
35: 72
36: 63
37: 53
38: 45
39: 36
40: 30
41: 23
42: 18
43: 13
44: 10
45: 7
46: 5
47: 3
48: 2
49: 1
50: 1

There exists a visualization script graphs.py to create graphs from this generated data. The script has commented examples and the data folder has pre calculated sum data.

Visualization Examples

All examples use the number set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}