Specializations of Grothendieck polynomials

We prove a formula for double Schubert and Grothendieck polynomials specialized to two rearrangements of the same set of variables. Our formula generalizes the usual formulas for Schubert and Grothendieck polynomials in terms of RC-graphs, and it gives immediate proofs of many other important properties of these polynomials.Comment: 4 pages, 1 figur

Specializations of Grothendieck polynomials

Let v,w ∈ Sn be permutations and let Sw(x; y) and Gw(a; b) denote the double Schubert and Grothendieck polynomials of Lascoux and Schutzenberger [11]. The goal of this note is to prove a formula for the specializations of these polynomials to different rearrangements of the same set of variables