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Questions related to combinatorics and discrete mathematical structures
8
votes
Accepted
Stability for couples in the Stable Matching Problem
Yes, it is stable. It doesn't need to assign the optimal choices for both sides. To break a marriage you need two willing parties, unhappiness of one side in a marriage doesn't make it unstable here.
3
votes
Accepted
How many segmentations are possible for a string length N?
There are n-1 points where you can break the string. Each is independent of the others. Therefore there are $2^{n-1}$ possibilities to break the string.
38
votes
Accepted
Why are there more non-computable functions than computable ones?
The are countably many computable functions:
Each computable function has at least one algorithm.
Each algorithm has a finite description using symbols from a finite set, e.g. finite binary strings …