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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.

2 votes

Structures that turn out to exhibit a symmetry even though their definition doesn't

Let $r_4(n)$ be the number of $4$-tuples $a,b,c,d\in \bf Z$ satisfying $a^2+b^2+c^2+d^2=n$. Then $\sum_{n\geq 0}r_4(n)e^{2\pi i\, nz}dz$ is a holomorphic differential form on the upper half-plane tha …
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