On trees with the same restricted U-polynomial and the Prouhet–Tarry–Escott problem

This paper focuses on the well-known problem due to Stanley of whether two non-isomorphic trees can have the same U-polynomial (or, equivalently, the same chromatic symmetric function). We consider the Uk-polynomial, which is a restricted version of U-polynomial, and construct, for any given k, non-...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Discrete mathematics Jg. 340; H. 6; S. 1435 - 1441
Hauptverfasser: Aliste-Prieto, José, de Mier, Anna, Zamora, José
Format: Journal Article Verlag
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.06.2017
Schlagworte:
05 Combinatorics
05C Graph theory
05E Algebraic combinatorics
[formula omitted]-polynomial
Chromatic symmetric function
Classificació AMS
Combinatorial analysis
Combinatòria
Graph polynomials
Matemàtica discreta
Matemàtiques i estadística
Polinomis
Polynomials
Prouhet–Tarry– Escott problem
UU-polynomial
Àrees temàtiques de la UPC
Prouhet–Tarry– Escott problem
Graph polynomials
Chromatic symmetric function
U-polynomial
ISSN:0012-365X, 1872-681X
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:This paper focuses on the well-known problem due to Stanley of whether two non-isomorphic trees can have the same U-polynomial (or, equivalently, the same chromatic symmetric function). We consider the Uk-polynomial, which is a restricted version of U-polynomial, and construct, for any given k, non-isomorphic trees with the same Uk-polynomial. These trees are constructed by encoding solutions of the Prouhet–Tarry–Escott problem. As a consequence, we find a new class of trees that are distinguished by the U-polynomial up to isomorphism.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2016.09.019