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This question is a mirror of the question Sum of subsets which I found interesting. The problem is like this:
Let , how many subsets with k elements that are having the sum of value r?
For instance, if n = 6, k = 3, r = 10:
The following sets: ...
This paper is inspired by this post. It asked how to count the number of solutions of the equation with non-negative integral solution:
x_1 + ... + x_k = n
without using the standard method of line and dot counting. I transform the problem into a partial difference equation, ...
This article provides and describes a Python function to list all the derangements of a multiset.
