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The authors give a combinatorial expansion of a Schubert homology class in the affine Grassmannian $\mathrm Gr _ \mathrm SL _k $ into Schubert homology classes in $\mathrm Gr _ \mathrm SL _ k 1 $. This is achieved by studying the combinatorics of a new class of partitions called $k$-shapes, which interpolates between $k$-cores and $k 1$-cores.