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Questions related to permutations, bijections from a finite (or sometimes infinite) set to itself.

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How many Shapes are possible to create using Voxels?

I think this is a permutations with repetition problem, and so far, this is the equation I came with: $$ a= ( \sum_{n=0}^{A} P_{A}^{A-n,n} )^Z $$ Where: $ a= $ Number of possible arrangements $ Z … = $ Value of the number of layers equal to $z/t$ $ A= $ Area of each layer equal to $(x/t)(y/t)$ $ P_n^{n_1,...,n_r}=$ Notation for Permutations with Repetition So, for example, if it is used the values …
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