Refined Dual Stable Grothendieck Polynomials and Generalized Bender-Knuth Involutions
نویسندگان
چکیده
منابع مشابه
Refined Dual Stable Grothendieck Polynomials and Generalized Bender-Knuth Involutions
The dual stable Grothendieck polynomials are a deformation of the Schur functions, originating in the study of the K-theory of the Grassmannian. We generalize these polynomials by introducing a countable family of additional parameters, and we prove that this generalization still defines symmetric functions. For this fact, we give two self-contained proofs, one of which constructs a family of i...
متن کاملStable Grothendieck Polynomials and K-theoretic Factor Sequences
We give a nonrecursive combinatorial formula for the expansion of a stable Grothendieck polynomial in the basis of stable Grothendieck polynomials for partitions. The proof is based on a generalization of the EdelmanGreene insertion algorithm. This result is applied to prove a number of formulas and properties for K-theoretic quiver polynomials and Grothendieck polynomials. In particular we for...
متن کاملRefined restricted involutions
Define I n(α) to be the set of involutions of {1, 2, . . . , n} with exactly k fixed points which avoid the pattern α ∈ Si, for some i ≥ 2, and define I n(∅;α) to be the set of involutions of {1, 2, . . . , n} with exactly k fixed points which contain the pattern α ∈ Si, for some i ≥ 2, exactly once. Let in(α) be the number of elements in I k n(α) and let i k n(∅;α) be the number of elements in...
متن کاملAnother refinement of the Bender-Knuth (ex-)conjecture
We compute the generating function of column-strict plane partitions with parts in {1, 2, . . . , n}, at most c columns, p rows of odd length and k parts equal to n. This refines both, Krattenthaler’s [10] and the author’s [5] refinement of the Bender-Knuth (ex-)Conjecture. The result is proved by an extension of the method for proving polynomial enumeration formulas which was introduced by the...
متن کاملFactorial Grothendieck Polynomials
In this paper, we study Grothendieck polynomials from a combinatorial viewpoint. We introduce the factorial Grothendieck polynomials, analogues of the factorial Schur functions and present some of their properties, and use them to produce a generalisation of a Littlewood-Richardson rule for Grothendieck polynomials.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/5737