Exact sampling of uniform RBPDs

Develop an exact sampler for uniformly random reduced bumpless pipe dreams, overcoming the failure of standard monotone CFTP due to non-sublattice and non-monotonicity obstacles.

Background

The natural embedding into the ASM lattice suggests CFTP, but reducedness breaks the sublattice property and invalidates the monotone coupling, leading to false coalescence. The paper therefore resorts to MCMC with additional droop moves for approximate sampling.

A method achieving exact sampling without these monotonicity issues remains to be found.

References

Neither $2\times 2$ flips nor droops/undroops seem to be appropriate ingredients for an exact sampling algorithm with CFTP, and so the question of exact sampling of uniform RBPDs also remains open.

— Computation and sampling for Schubert specializations  (2603.20104 - Anderson et al., 20 Mar 2026) in Section 6.4