Pieri's formula describes the intersection product of a Schubert cycle by a special Schubert cycle on a Grassmannian.We present a new geometric proof,exhibiting an explicit chain of rational equivalences from a suitable sum of distinct Schubert cyclesto the intersection of a Schubert cycle with a specialSchubert cycle. The geometry of these rational equivalencesindicates a link to a combinatorial proof of Pieri's formula usingSchensted insertion.
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