This tag is for basic questions about the study of finite or countable discrete structures — specifically how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions. ...

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Traverse resultant 2d array after integer partition

I have used the solution of integer partitioning using dynamic programming explained in this post and in this article. Following is the resultant matrix when N is equal to 6: $$\begin{bmatrix} 1 ...
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Blocking lines of length $5$ in a $7 \times 8$ matrix; how can we know the solutions have a specific form?

A friend shared with me the following puzzle he encountered in a Chinese math competition: In a $7 \times 8$ matrix, we place tokens so that any straight line of length $5$ (horizontal, vertical, ...