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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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A conjecture on partitions
Let $p>q$ be two prime numbers. Let $\lambda$ be a partition whose $p$-core is $\lambda_p$ and $q$-core is $\lambda_q$. Assume that $|\lambda|>|\lambda_p|+|\lambda_q|$. Is it true that there always ex …