The main theorem here is the -theoretic analogue of the cohomological ``stable double component formula'' for quiver polynomials in [KMS]. This -theoretic version is still in terms of lacing diagrams, but nonminimal diagrams contribute terms of higher degree. The motivating consequence is a conjecture of Buch [B1] on the sign alternation of the coefficients appearing in his expansion of quiver -polynomials in terms of stable Grothendieck polynomials for partitions.
Ezra Miller. "Alternating formulas for -theoretic quiver polynomials." Duke Math. J. 128 (1) 1 - 17, 15 May 2005. https://doi.org/10.1215/S0012-7094-04-12811-8