Geodesic
A partial Horn recursion in the cohomology of flag varieties
Journal of Algebraic Combinatorics, Tome 30 (2009) no. 1, pp. 1-17.

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Summary: Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of complex flag varieties are characterized by inequalities parameterized by similar non-vanishing products in the cohomology of "smaller" flag varieties. We consider the type A partial flag variety and find that its cohomology exhibits a Horn recursion on a certain deformation of the cup product defined by Belkale and Kumar (Invent. Math. 166:185-228, 2006). We also show that if a product of Schubert classes is non-vanishing on this deformation, then the associated structure constant can be written in terms of structure constants coming from induced Grassmannians.
Keywords: keywords partial flag varieties, Horn recursion, Schubert varieties, Schubert calculus, Littlewood-Richardson coefficients, structure constants 
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Richmond, Edward. A partial Horn recursion in the cohomology of flag varieties. Journal of Algebraic Combinatorics, Tome 30 (2009) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/JAC_2009__30_1_a5/