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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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On the existence of symmetric matrices with prescribed number of 1's on each row

We are considering the following problem: Given an integer $n$ and a sequence of integers $r_i,\ 1\le i\le n$, with $0\le r_i\le n-1$ does there exists a symmetric matrix $A$ such that the diagonal el …