A horizontal-strip LLT polynomial is determined by its weighted graph

DOI10.5070/c63362793arXiv2110.07984OpenAlexW3205000942MaRDI QIDQ6204692

Foster Tom

Publication date: 2 April 2024

Published in: Combinatorial Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.07984

zbMATH Keywords

weighted graphinterval graphSchur functionHall-Littlewood polynomialchromatic symmetric functionLLT polynomial

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Coloring of graphs and hypergraphs (05C15)

Cites Work

• Chromatic quasisymmetric functions
• Proper caterpillars are distinguished by their chromatic symmetric function
• A combinatorial formula for the character of the diagonal coinvariants
• LLT polynomials, chromatic quasisymmetric functions and graphs with cycles
• LLT polynomials, elementary symmetric functions and melting lollipops
• Extended chromatic symmetric functions and equality of ribbon Schur functions
• A combinatorial expansion of vertical-strip LLT polynomials in the basis of elementary symmetric functions
• A deletion-contraction relation for the chromatic symmetric function
• Cyclic sieving, skew Macdonald polynomials and Schur positivity
• Melting lollipop chromatic quasisymmetric functions and Schur expansion of unicellular LLT polynomials
• The Roberts characterization of proper and unit interval graphs
• Decomposable compositions, symmetric quasisymmetric functions and equality of ribbon Schur functions
• A vertex-weighted Tutte symmetric function, and constructing graphs with equal chromatic symmetric function
• A note on distinguishing trees with the chromatic symmetric function
• Ribbon tableaux, Hall–Littlewood functions, quantum affine algebras, and unipotent varieties
• A proof of the shuffle conjecture
• A combinatorial formula for Macdonald polynomials
• A combinatorial Schur expansion of triangle-free horizontal-strip LLT polynomials
• A Proof of the Extended Delta Conjecture

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