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Main Question or Discussion Point
Hello,
The problem I came up with deals with the structures that can be obtained by joining squares side to side or corner to corner. Specifically to this problem, structures, that are symmetrical to each other, are regarded the same.
Ideally, I am looking for a formula that will tell how many structures can be made with n given squares. However, I am aware of the problem's complexity (this is the nature of partition problems...), so,at least, it will be comforting, if someone comes up with an insight about what happens "behind the scenes" in the problem.
One can easily observe that the n+1 structures can be generated from the n structures. By applying this principle, I was able to draw all the unique structures up to n=5. Then, I tried to classify them by the minimal rectangle that encloses the structure, and still lead to no progress.
I ran out of new strategies for a solution, and I am asking for another perspective on the problem.
The problem I came up with deals with the structures that can be obtained by joining squares side to side or corner to corner. Specifically to this problem, structures, that are symmetrical to each other, are regarded the same.
Ideally, I am looking for a formula that will tell how many structures can be made with n given squares. However, I am aware of the problem's complexity (this is the nature of partition problems...), so,at least, it will be comforting, if someone comes up with an insight about what happens "behind the scenes" in the problem.
One can easily observe that the n+1 structures can be generated from the n structures. By applying this principle, I was able to draw all the unique structures up to n=5. Then, I tried to classify them by the minimal rectangle that encloses the structure, and still lead to no progress.
I ran out of new strategies for a solution, and I am asking for another perspective on the problem.
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