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We develop Pieri type as well as Murnaghan--Nakayama type formulas forequivariant Chern--Schwartz--MacPherson classes of Schubert cells in theclassical flag variety. These formulas include as special cases many previouslyknown multiplication formulas for Chern--Schwartz--MacPherson classes orSchubert classes. We apply the equivariant Murnaghan--Nakayama formula to theenumeration of rim hook tableaux.

Pieri and Murnaghan--Nakayama type Rules for Chern classes of Schubert Cells