Lollipop and Lariat Symmetric Functions

DOI10.1137/17M1144805zbMath1387.05264arXiv1702.06974OpenAlexW2963840126MaRDI QIDQ4641758

Samantha Dahlberg, Stephanie Van Willigenburg

Publication date: 18 May 2018

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

Full work available at URL: https://arxiv.org/abs/1702.06974

zbMATH Keywords

Schur functionlollipop graphelementary symmetric functionchromatic symmetric functionlariat graph

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Coloring of graphs and hypergraphs (05C15)

Related Items (25)

On the \(e\)-positivity of trees and spiders ⋮ A combinatorial expansion of vertical-strip LLT polynomials in the basis of elementary symmetric functions ⋮ Positivity of chromatic symmetric functions associated with Hessenberg functions of bounce number 3 ⋮ On \(e\)-positivity and \(e\)-unimodality of chromatic quasisymmetric functions ⋮ Spiders and their kin: an investigation of Stanley's chromatic symmetric function for spiders and related graphs ⋮ A vertex-weighted Tutte symmetric function, and constructing graphs with equal chromatic symmetric function ⋮ Bases of the equivariant cohomologies of regular semisimple Hessenberg varieties ⋮ Marked Graphs and the Chromatic Symmetric Function ⋮ A combinatorial formula for the Schur coefficients of chromatic symmetric functions ⋮ A deletion-contraction relation for the chromatic symmetric function ⋮ The \(e\)-positivity of two classes of cycle-chord graphs ⋮ Robinson-Schensted correspondence for unit interval orders ⋮ LLT polynomials, elementary symmetric functions and melting lollipops ⋮ Chromatic symmetric functions in noncommuting variables revisited ⋮ Melting lollipop chromatic quasisymmetric functions and Schur expansion of unicellular LLT polynomials ⋮ Extended chromatic symmetric functions and equality of ribbon Schur functions ⋮ Schur and \(e\)-positivity of trees and cut vertices ⋮ LLT polynomials, chromatic quasisymmetric functions and graphs with cycles ⋮ Chromatic posets ⋮ On $e$-Positivity and $e$-Unimodality of Chromatic Quasi-symmetric Functions ⋮ Modular relations of the Tutte symmetric function ⋮ Resolving Stanley's \(e\)-positivity of claw-contractible-free graphs ⋮ The second cohomology of regular semisimple Hessenberg varieties from GKM theory ⋮ A Complete Multipartite Basis for the Chromatic Symmetric Function ⋮ The \(e\)-positivity and Schur positivity of some spiders and broom trees

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