Séminaire Lotharingien de Combinatoire, 93B.66 (2025), 12 pp.

Yibo Gao and Hai Zhu

Boolean Structure Constants

Abstract. The Schubert problem asks for combinatorial models to compute structure constants of the cohomology ring with respect to the Schubert classes, and has been an important open problem in algebraic geometry and combinatorics that guided fruitful research in decades. In this paper, we provide an explicit formula for the (equivariant) Schubert structure constants c_uv^w across all Lie types when the elements u,v,w are boolean. In particular, in type A, all Schubert structure constants on boolean elements are either 0 or 1.

Received: November 15, 2024. Accepted: February 15, 2025. Final version: April 1, 2025.

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