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We give positive combinatorial descriptions of Schubert structure constants$c_{u,v}^w$ for the full flag variety in type $A_{n-1}$ when $u$ and $v$ formwhat we refer to as a "$(p,q)$-pair" ($p+q=n$). The key observation is that acertain subset of the $GL(p,\mathbb{C}) \times GL(q,\mathbb{C})$-orbit closureson the flag variety (those satisfying an easily stated pattern avoidancecondition) are Richardson varieties. The result on structure constants followswhen one combines this observation with a theorem of Brion concerningintersection numbers of spherical subgroup orbit closures and Schubertvarieties.

GL(p) x GL(q)-orbit closures on the flag variety and Schubert structure constants for (p,q)-pairs