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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

2 votes
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206 views

Real-rooted polynomials with coefficient constraints

My question is whether there exists $(a_0, a_1, \ldots, a_{2n-1}) \in \mathbb{R}_{+}^{2n}$ such that (1). $a_{2k} + a_{2k+1} = \binom{3n-1}{3k} + \binom{3n-1}{3k+1} + \binom{3n-1}{3k+2}$ for all $0 …