A Formula for K-Theory Truncation Schubert Calculus

Define a truncation rt(p) of a polynomial p in {x1, x2, x3, . . .} as the polynomial with all but the first t variables set to zero. In certain good cases, the truncation of a Schubert or Grothendieck polynomial may again be a Schubert or Grothendieck polynomial. We use this phenomenon to give subtraction-free formulae for certain Schubert structure constants in K(Flags(C)), in particular generalizing those from [Kogan, ’00] in which only cohomology was treated, and from [Buch, ’02] on the Grassmannian case. The terms in the answer are computed using “marching” operations on permutation diagrams.