The Peterson comparison formula proved by Woodward relates the three-pointedGromov-Witten invariants for the quantum cohomology of partial flag varietiesto those for the complete flag. Another such comparison can be obtained bycomposing a combinatorial version of the Peterson isomorphism with a result ofLapointe and Morse relating quantum Littlewood-Richardson coefficients for theGrassmannian to k-Schur analogs in the homology of the affine Grassmannianobtained by adding rim hooks. We show that these comparisons on quantumcohomology are equivalent, up to Postnikov's strange duality isomorphism.<br
