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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

4 votes

What is the smallest size of a shape in which all fixed $n$-polyominos can fit?

Proof outline for $\Omega(n^{2-\varepsilon})$ Choose a positive integer $k$ which will determine that $\varepsilon=\frac{1}{k}$. Now consider the problem of embedding the 1 dimensional $k$-block shape …
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