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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.
Kaveh's user avatar
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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.
Kaveh's user avatar
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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 …
Kaveh's user avatar
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