On trees with the same restricted \(U\)-polynomial and the Prouhet-Tarry-Escott problem

DOI10.1016/j.disc.2016.09.019zbMath1369.05031arXiv1509.09210OpenAlexW2186139259MaRDI QIDQ2400582

Anna de Mier, José Aliste-Prieto, José Zamora

Publication date: 29 August 2017

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

Full work available at URL: https://arxiv.org/abs/1509.09210

zbMATH Keywords

graph polynomials\(U\)-polynomialchromatic symmetric functionProuhet-Tarry-Escott problem

Mathematics Subject Classification ID

Trees (05C05) Graph polynomials (05C31) Symmetric functions and generalizations (05E05) Coloring of graphs and hypergraphs (05C15)

Related Items (16)

On the \(e\)-positivity of trees and spiders ⋮ A vertex-weighted Tutte symmetric function, and constructing graphs with equal chromatic symmetric function ⋮ A note on distinguishing trees with the chromatic symmetric function ⋮ Marked Graphs and the Chromatic Symmetric Function ⋮ Quasisymmetric functions distinguishing trees ⋮ A deletion-contraction relation for the chromatic symmetric function ⋮ On the smallest trees with the same restricted \(U\)-polynomial and the rooted \(U\)-polynomial ⋮ An improvement of Prouhet’s 1851 result on multigrade chains ⋮ Lollipop and Lariat Symmetric Functions ⋮ A tree distinguishing polynomial ⋮ Tutte polynomials for directed graphs ⋮ On graphs with the same restricted \(U\)-polynomial and the \(U\)-polynomial for rooted graphs ⋮ Schur and \(e\)-positivity of trees and cut vertices ⋮ Chromatic posets ⋮ Modular relations of the Tutte symmetric function ⋮ A Complete Multipartite Basis for the Chromatic Symmetric Function

Cites Work

• Unnamed Item
• Proper caterpillars are distinguished by their chromatic symmetric function
• Graphs with equal chromatic symmetric functions
• Computational excursions in analysis and number theory
• Intersection theory for graphs
• A weighted graph polynomial from chromatic invariants of knots
• The Prouhet-Tarry-Escott problem revisited
• Polychromatic polynomials
• The polychromate and a chord diagram polynomial
• A symmetric function generalization of the chromatic polynomial of a graph
• Contraction-deletion invariants for graphs
• On distinguishing trees by their chromatic symmetric functions
• Prouhet's 1851 Solution of the Tarry-Escott Problem of 1910
• Equal sums of like powers

This page was built for publication: On trees with the same restricted \(U\)-polynomial and the Prouhet-Tarry-Escott problem