2019
DOI: 10.1215/00127094-2018-0043
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Three combinatorial formulas for type A quiver polynomials and K-polynomials

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 Rimányi.

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Cited by 3 publications
(3 citation statements)
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“…These characteristic classes (and their K-theoretic analogues) have a rich history in their own right; they exhibit remarkable combinatorial and geometric properties and have connections to many other areas of algebraic combinatorics and algebraic geometry. The author suggests the seminal work of Buch-Fulton [BF99], as well as the more recent papers [Buc08] and [KKR19] (and references therein), as a starting point on quiver polynomials.…”
Section: Dynkin Quiversmentioning
confidence: 99%
See 1 more Smart Citation
“…These characteristic classes (and their K-theoretic analogues) have a rich history in their own right; they exhibit remarkable combinatorial and geometric properties and have connections to many other areas of algebraic combinatorics and algebraic geometry. The author suggests the seminal work of Buch-Fulton [BF99], as well as the more recent papers [Buc08] and [KKR19] (and references therein), as a starting point on quiver polynomials.…”
Section: Dynkin Quiversmentioning
confidence: 99%
“…On the other hand, the following result further relates the fundamental class of η m directly to Dynkin quiver polynomials. We note that the quiver polynomials have a rich history in their own right, and exhibit interesting geometric and combinatorial properties; see e.g., [Buc08,KKR19] and references therein. Corollary 6.7.…”
Section: Structure Theorems For Cohamentioning
confidence: 99%
“…Note that this definition clearly identifies a lacing diagram w as a specific point of rep Q (d). For details of our conventions, which may differ from other authors for technical reasons, see [KKR,§2.8]. The matrix representation of the leftmost lacing diagram in Figure 1 is…”
Section: Lacing Diagramsmentioning
confidence: 99%