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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.
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Matrix inequality $a X \succeq arcsin(X)$ for some $a > 0$
Let $X \in S^{n}_{+}$ be a positive semi-definite matrix with $X_{ii} = 1$ for all $i \leq n$ (thus $X$ is a correlation matrix).
Since $X$ is positive semi-definite, we have $|X_{ij}| \leq 1$ for any …