Related papers: Factorial Grothendieck Polynomials
We give a combinatorial rule for calculating the coefficients in the expansion of a product of two factorial Schur functions. It is a special case of a more general rule which also gives the coefficients in the expansion of a skew factorial…
We give new formulas for Grothendieck polynomials of two types. One type expresses any specialization of a Grothendieck polynomial in at least two sets of variables as a linear combination of products Grothendieck polynomials in each set of…
We formulate a nonrecursive combinatorial rule for the expansion of the stable Grothendieck polynomials of [Fomin-Kirillov '94] in the basis of stable Grothendieck polynomials for partitions. This gives a common generalization, as well as…
This report formulates a conjectural combinatorial rule that positively expands Grothendieck polynomials into Lascoux polynomials. It generalizes one such formula expanding Schubert polynomials into key polynomials, and refines another one…
We give a proof of the generalized Cauchy identity for double Grothendieck polynomials, a combinatorial interpretation of the stable double Grothendieck polynomials in terms of triples of tableaux, and an interpolation between the stable…
We use Bott-Samelson resolutions of Schubert varieties in Grassmannians along with equiariant localization techniques to show that the factorial Schur functions and the factorial Grothendieck polynomials represent Schubert classes in…
Macdonald polynomials are orthogonal polynomials associated to root systems, and in the type A case, the symmetric kind is a common generalization of Schur functions, Macdonald spherical functions, and Jack polynomials. We use the…
We study the Littlewood-Richardson coefficients of double Grothendieck polynomials indexed by Grassmannian permutations. Geometrically, these are the structure constants of the equivariant $K$-theory ring of Grassmannians. Representing the…
We give an algebraic proof of the determinant formulas for factorial Grothendieck polynomials obtained by Hudson--Ikeda--Matsumura--Naruse and by Hudson--Matsumura.
For a given skew shape, we build a crystal graph on the set of all reverse plane partitions that have this shape. As a consequence, we get a simple extension of the Littlewood-Richardson rule for the expansion of the corresponding dual…
We consider the Grothendieck polynomials appearing in the K-theory of Grassmannians, which are analogs of Schur polynomials. This paper aims to establish a version of the Murnaghan-Nakayama rule for Grothendieck polynomials of the…
Stable Grothendieck polynomials can be viewed as a K-theory analog of Schur polynomials. We extend stable Grothendieck polynomials to a two-parameter version, which we call canonical stable Grothendieck functions. These functions have the…
The product of any finite number of factorial Schur functions can be expanded as a $Z[y]$-linear combination of Schur functions. We give a rule for computing the coefficients in such an expansion which generalizes a specialization of the…
We introduce a family of rings of symmetric functions depending on an infinite sequence of parameters. A distinguished basis of such a ring is comprised by analogues of the Schur functions. The corresponding structure coefficients are…
We pose the question of what is the best generalization of the factorial and the binomial coefficient. We give several examples, derive their combinatorial properties, and demonstrate their interrelationships. On cherche ici \`a…
This paper gives a tableau formula for expanding the product of a Lascoux polynomial and a stable Grothendieck polynomial into Lascoux polynomials. Lascoux and stable Grothendieck polynomials are inhomogeneous analogues of key polynomials…
We prove a formula for double Schubert and Grothendieck polynomials specialized to two rearrangements of the same set of variables. Our formula generalizes the usual formulas for Schubert and Grothendieck polynomials in terms of RC-graphs,…
We give a combinatorial expansion of the stable Grothendieck polynomials of skew Young diagrams in terms of skew Schur functions, using a new row insertion algorithm for set-valued semistandard tableaux of skew shape. This expansion unifies…
Skew stable Grothendieck polynomials are $K$-theoretic analogues of skew Schur polynomials. We give a free-fermionic presentation of skew stable Grothendieck polynomials and their dual symmetric functions. By using our presentation, we…
The aim of this note is to give some factorization formulas for different versions of the Macdonald polynomials when the parameter t is specialized at roots of unity, generalizing those existing for Hall-Littlewood functions.