Three combinatorial formulas for type A quiver polynomials and K-polynomials
Ryan Kinser, Allen Knutson, Jenna Rajchgot
TL;DR
This paper develops combinatorial formulas for type A quiver polynomials and K-polynomials, extending previous formulas to arbitrary orientations and confirming a conjecture by Buch and Rimányi.
Contribution
It generalizes three formulas for quiver polynomials to arbitrary orientations and proves the K-theoretic component formula conjectured by Buch and Rimányi.
Findings
Provided combinatorial formulas for multidegree and K-polynomial of type A quiver loci.
Extended known formulas from equioriented to arbitrarily oriented quivers.
Confirmed the K-theoretic component formula conjectured by Buch and Rimányi.
Abstract
We provide combinatorial formulas for the multidegree and K-polynomial of an arbitrarily oriented type A quiver locus. These formulas are generalizations of three of Knutson-Miller-Shimozono's formulas from the equioriented setting; in particular, we prove the K-theoretic component formula conjectured by Buch and Rim\'anyi.
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