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

We develop Pieri type as well as Murnaghan–Nakayama type formulas for equivariant Chern–Schwartz–MacPherson classes of Schubert cells in the classical flag variety. These formulas include as special cases many previously known multiplication formulas for Chern–Schwartz–MacPherson classes or Schubert classes. We apply the equivariant Murnaghan–Nakayama formula to the enumeration of rim hook tableaux.