The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture

zbMath1417.14007arXiv1709.06736MaRDI QIDQ5925192

Martha Precup, Megumi Harada

Publication date: 15 May 2019

Published in: Séminaire Lotharingien de Combinatoire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.06736

zbMATH Keywords

symmetric functionsHessenberg varietiesStanley-Stembridge conjecture

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Grassmannians, Schubert varieties, flag manifolds (14M15)

Related Items (16)

On \(e\)-positivity and \(e\)-unimodality of chromatic quasisymmetric functions ⋮ Hessenberg varieties, Slodowy slices, and integrable systems ⋮ Hessenberg varieties associated to ad-nilpotent ideals ⋮ A Survey of Recent Developments on Hessenberg Varieties ⋮ Lollipop and Lariat Symmetric Functions ⋮ LLT polynomials, elementary symmetric functions and melting lollipops ⋮ Unit interval orders and the dot action on the cohomology of regular semisimple Hessenberg varieties ⋮ Chromatic symmetric functions in noncommuting variables revisited ⋮ The volume polynomial of regular semisimple Hessenberg varieties and the Gelfand-Zetlin polytope ⋮ Melting lollipop chromatic quasisymmetric functions and Schur expansion of unicellular LLT polynomials ⋮ Schur and \(e\)-positivity of trees and cut vertices ⋮ Linear relations on LLT polynomials and their \(k\)-Schur positivity for \(k=2\) ⋮ Chromatic posets ⋮ On $e$-Positivity and $e$-Unimodality of Chromatic Quasi-symmetric Functions ⋮ A new formula for Stanley's chromatic symmetric function for unit interval graphs and E-positivity for triangular ladder graphs ⋮ Classes of graphs with \(e\)-positive chromatic symmetric function

Cites Work

• Unnamed Item
• Unnamed Item
• Chromatic quasisymmetric functions
• Affine pavings of Hessenberg varieties for semisimple groups
• On immanants of Jacobi-Trudi matrices and permutations with restricted position
• A symmetric function generalization of the chromatic polynomial of a graph
• Incomparability graphs of \((3+1)\)-free posets are \(s\)-positive
• Hessenberg Varieties
• Unit interval orders and the dot action on the cohomology of regular semisimple Hessenberg varieties

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