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arXiv · 2608.17378

Non-vanishing of Single, Double, and Triple Schubert Structure Constants

Yiming Chen·Neil J. Y. Fan·Rui Xiong·Ming Yao
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Abstract

The Schubert vanishing problem asks whether the single Schubert coefficients $c_{u,v}^w$ are zero. In this paper, we consider the non-vanishing problems of double Schubert coefficients $c_{u,v}^w(t)$ and triple Schubert coefficients $c_{u,v}^w(t;y)$. We show that the non-vanishing of $c_{u,v}^w(t;y)$ is completely determined by the non-vanishing of single Schubert coefficients. As a byproduct, we obtain the saturation property of the triple Littlewood--Richardson coefficients $c_{\lambda,\mu}^\nu(t;y)$. Moreover, we pose a conjecture asserting that the non-vanishing of $c_{u,v}^w(t)$ is also determined by the non-vanishing of single or triple Schubert coefficients. We prove a one-side inclusion of the conjecture. For the reverse inclusion, we show that the conjecture holds for the following three cases: the Pieri case, the separated descents case, and the inverse Grassmannian case.

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Yiming Chen, Neil J. Y. Fan, Rui Xiong, Ming Yao. 2026-08-18. Non-vanishing of Single, Double, and Triple Schubert Structure Constants. https://arxiv.org/abs/2608.17378

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