Symmetric Grothendieck polynomials, skew Cauchy identities, and dual filtered Young graphs

DOI10.1016/j.jcta.2018.09.006zbMath1400.05264arXiv1711.09544OpenAlexW2963250888MaRDI QIDQ1621432

Damir Yeliussizov

Publication date: 8 November 2018

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.09544

zbMATH Keywords

symmetric functionsSchur polynomialsGrothendieck polynomialsPieri rulesCauchy identitiesdual filtered graphs

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05)

Related Items (16)

Free-fermions and skew stable Grothendieck polynomials ⋮ Enriched set-valued \(P\)-partitions and shifted stable Grothendieck polynomials ⋮ Combinatorial formulas for shifted dual stable Grothendieck polynomials ⋮ Expanding \(K\) theoric Schur \(Q\)-functions ⋮ Free fermions and canonical Grothendieck polynomials ⋮ Free fermions and Schur expansions of multi-Schur functions ⋮ MacMahon’s statistics on higher-dimensional partitions ⋮ Tableau formulas for skew Grothendieck polynomials ⋮ Vertex models for canonical Grothendieck polynomials and their duals ⋮ Enumeration of plane partitions by descents ⋮ Random plane partitions and corner distributions ⋮ Integrable models and \(K\)-theoretic pushforward of Grothendieck classes ⋮ Crystal structures for symmetric Grothendieck polynomials ⋮ Positive specializations of symmetric Grothendieck polynomials ⋮ Dual Grothendieck polynomials via last-passage percolation ⋮ Determinantal formulas for dual Grothendieck polynomials

Cites Work

• Unnamed Item
• Unnamed Item
• Skew Pieri rules for Hall-Littlewood functions
• Remarks on the paper ``skew Pieri rules for Hall-Littlewood functions by Konvalinka and Lauve
• Duality and deformations of stable Grothendieck polynomials
• Branching rules for symmetric functions and \(\mathfrak{sl}_n\) basic hypergeometric series
• A Pieri rule for skew shapes
• On a family of symmetric rational functions
• Robinson-Schensted algorithms for skew tableaux
• Combinatorics of \(K\)-theory via a \(K\)-theoretic Poirier-Reutenauer bialgebra
• Duality of graded graphs
• Noncommutative Schur functions and their applications
• Quasisymmetric and noncommutative skew Pieri rules
• A Littlewood-Richardson rule for the \(K\)-theory of Grassmannians.
• Schur operators and Knuth correspondences
• Combinatorial aspects of the \(K\)-theory of Grassmannians
• Skew Littlewood-Richardson Rules from Hopf Algebras
• Differential Posets
• Combinatorial Hopf Algebras and K-Homology of Grassmanians

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