# Grothendieck polynomials and quiver formulas

Research paper by Anders Skovsted Buch, Andrew Kresch, Harry Tamvakis, Alexander Yong

Indexed on: 27 Jun '03Published on: 27 Jun '03Published in: Mathematics - Combinatorics

#### Abstract

Fulton's universal Schubert polynomials give cohomology formulas for a class of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver formula of Buch expresses the structure sheaves of these loci as integral linear combinations of products of stable Grothendieck polynomials. We prove an explicit combinatorial formula for the coefficients, which shows that they have alternating signs. Our result is applied to obtain new expansions for the Grothendieck polynomials of Lascoux and Sch\"utzenberger.