Alternating signs of quiver coefficients

I will speak about K-theoretic generalizations of the component formulas of Knutson, Miller, and Shimozono, which show that K-theoretic quiver coefficients have alternating signs. I will also explain new variants of the factor sequences conjecture. If time allows, I will furthermore discuss a proof of a conjecture of Knutson, Miller, and Shimozono, which states that their double ratio formula agrees with the original quiver formulas.