PIERIS FORMULA VIA EXPLICIT RATIONAL EQUIVALENCE

Pieri's formula describes the intersection product of a Schubert cycle by a special Schubert cycle on a Grassmannian. We present a new geome tric proof, exhibiting an explicit chain of rational equivalences from a suitable sum of distinct Schubert cycles to the intersection of a S chubert cycle with a special Schubert cycle. The geometry of these rat ional equivalences indicates a link to a combinatorial proof of Pieri' s formula using Schensted insertion.