J. De Loera & T. McAllister and K. D. Mulmuley & H. Narayanan & M. Sohoni independently proved that determining the vanishing of Littlewood–Richardson coefficients has strongly polynomial time computational complexity. Viewing these as Schubert calculus numbers, we prove the generalization to the Littlewood–Richardson polynomials that control equivariant cohomology of Grassmannians. We construct a polytope using the edge-labeled tableau rule of H. Thomas, A. Yong. Our proof then combines a saturation theorem of D. Anderson, E. Richmond, A. Yong, a reading order independence property, and É. Tardos’ algorithm for combinatorial linear programming.

中文翻译：

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Littlewood-Richardson 多项式的消失在 P 中

J. De Loera & T. McAllister 和 KD Mulmuley & H. Narayanan & M. Sohoni 独立证明了确定 Littlewood-Richardson 系数的消失具有很强的多项式时间计算复杂度。将这些视为舒伯特微积分数，我们证明了控制 Grassmannians 等变上同调的 Littlewood-Richardson 多项式的推广。我们使用 H. Thomas, A. Yong 的边缘标记画面规则构建了一个多面体。我们的证明然后结合了 D. Anderson、E. Richmond、A. Yong 的饱和定理、阅读顺序独立性和 É。用于组合线性规划的 Tardos 算法。