Combinatorics of \(K\)-theory via a \(K\)-theoretic Poirier-Reutenauer bialgebra

DOI10.1016/j.disc.2015.10.044zbMath1328.05193arXiv1404.4340OpenAlexW2176840706MaRDI QIDQ897304

Pavlo Pylyavskyy, Rebecca Patrias

Publication date: 17 December 2015

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.4340

zbMATH Keywords

\(K\)-theorysymmetric functionsbialgebra

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Symmetric functions and generalizations (05E05) Classical problems, Schubert calculus (14N15)

Related Items (17)

Symmetric Grothendieck polynomials, skew Cauchy identities, and dual filtered Young graphs ⋮ Genomic tableaux ⋮ Promotion of increasing tableaux: frames and homomesies ⋮ A crystal on decreasing factorizations in the 0-Hecke monoid ⋮ Crystal structures for canonical Grothendieck functions ⋮ Bijecting hidden symmetries for skew staircase shapes ⋮ On some properties of symplectic Grothendieck polynomials ⋮ Crystal for stable Grothendieck polynomials ⋮ Crystal structures for canonical and dual weak symmetric Grothendieck functions ⋮ Shifted Hecke insertion and \(K\)-theory of \(OG(n,2n+1)\) ⋮ Duality and deformations of stable Grothendieck polynomials ⋮ Crystal structures for symmetric Grothendieck polynomials ⋮ Linear compactness and combinatorial bialgebras ⋮ Dual filtered graphs ⋮ Positive specializations of symmetric Grothendieck polynomials ⋮ Bialgebras for Stanley symmetric functions ⋮ \(K\)-Knuth equivalence for increasing tableaux

Cites Work

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• \(K\)-theory of minuscule varieties
• Longest increasing subsequences, Plancherel-type measure and the Hecke insertion algorithm
• Noncommutative symmetric functions. VII: Free quasi-symmetric functions revisited
• A jeu de taquin theory for increasing tableaux, with application to \(K\)-theoretic Schubert calculus
• Representations of finite classical groups. A Hopf algebra approach
• Some partitions associated with a partially ordered set
• Noncommutative Schur functions and their applications
• A Littlewood-Richardson rule for the \(K\)-theory of Grassmannians.
• Stable Grothendieck polynomials and \(K\)-theoretic factor sequences
• Properties of four partial orders on standard Young tableaux
• The Direct Sum Map on Grassmannians and Jeu de Taquin for Increasing Tableaux
• Combinatorial Hopf Algebras and K-Homology of Grassmanians

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